Publications
Monographs

H. Neidhardt, A. Stephan, V.A. Zagrebnov, Chapter 13: Trotter Product Formula and Linear Evolution Equations on Hilbert Spaces, in: Analysis and Operator Theory, Th.M. Rassias , V.A. Zagrebnov , eds., 146 of Springer Optimization and Its Applications, Springer, Cham, 2019, pp. 271299, (Chapter Published), DOI 10.1007/9783030126612_13 .
Articles in Refereed Journals

W. Dreyer, P.É. Druet, P. Gajewski, C. Guhlke, Analysis of improved NernstPlanckPoisson models of compressible isothermal electrolytes, ZAMP Zeitschrift fur Angewandte Mathematik und Physik. ZAMP. Journal of Applied Mathematics and Physics. Journal de Mathematiques et de Physique Appliquees, 71 (2020), pp. 119/1119/68, DOI 10.1007/s00033020013415 .
Abstract
We consider an improved NernstPlanckPoisson model first proposed by Dreyer et al. in 2013 for compressible isothermal electrolytes in non equilibrium. The model takes into account the elastic deformation of the medium that induces an inherent coupling of mass and momentum transport. The model consists of convectiondiffusionreaction equations for the constituents of the mixture, of the NavierStokes equation for the barycentric velocity, and of the Poisson equation for the electrical potential. Due to the principle of mass conservation, crossdiffusion phenomena must occur and the mobility matrix (Onsager matrix) has a kernel. In this paper we establish the existence of a globalintime weak solution for the full model, allowing for a general structure of the mobility tensor and for chemical reactions with highly non linear rates in the bulk and on the active boundary. We characterise the singular states of the system, showing that the chemical species can vanish only globally in space, and that this phenomenon must be concentrated in a compact set of measure zero in time. With respect to our former study [DDGG16], we also essentially improve the a priori estimates, in particular concerning the relative chemical potentials. 
P.É. Druet, A. Jüngel, Analysis of crossdiffusion systems for fluid mixtures driven by a pressure gradient, SIAM Journal on Mathematical Analysis, 52 (2020), pp. 21792197, DOI 10.1137/19M1301473 .
Abstract
The convective transport in a multicomponent isothermal compressible fluid subject to the mass continuity equations is considered. The velocity is proportional to the negative pressure gradient, according to Darcy?s law, and the pressure is defined by a state equation imposed by the volume extension of the mixture. These model assumptions lead to a parabolichyperbolic system for the mass densities. The globalintime existence of classical and weak solutions is proved in a bounded domain with nopenetration boundary conditions. The idea is to decompose the system into a porousmediumtype equation for the volume extension and transport equations for the modified number fractions. The existence proof is based on parabolic regularity theory, the theory of renormalized solutions, and an approximation of the velocity field. 
O. Marquardt, M.A. Caro, Th. Koprucki, P. Mathé, M. Willatzen, Multiband k · p model and fitting scheme for ab initiobased electronic structure parameters for wurtzite GaAs, Phys. Rev. B., 101 (2020), pp. 235147/1235147/12, DOI 10.1103/PhysRevB.101.235147 .
Abstract
We develop a 16band k · p model for the description of wurtzite GaAs, together with a novel scheme to determine electronic structure parameters for multiband k · p models. Our approach uses lowdiscrepancy sequences to fit k · p band structures beyond the eightband scheme to most recent ab initio data, obtained within the framework for hybridfunctional density functional theory with a screenedexchange hybrid functional. We report structural parameters, elastic constants, band structures along highsymmetry lines, and deformation potentials at the Γ point. Based on this, we compute the bulk electronic properties (Γ point energies, effective masses, Luttingerlike parameters, and optical matrix parameters) for a tenband and a sixteenband k · p model for wurtzite GaAs. Our fitting scheme can assign priorities to both selected bands and k points that are of particular interest for specific applications. Finally, ellipticity conditions can be taken into account within our fitting scheme in order to make the resulting parameter sets robust against spurious solutions. 
D.H. Doan, A. Fischer, J. Fuhrmann, A. Glitzky, M. Liero, Driftdiffusion simulation of Sshaped currentvoltage relations for organic semiconductor devices, Journal of Computational Electronics, 19 (2020), pp. 11641174, DOI 10.1007/s10825020015056 .
Abstract
We present an electrothermal driftdiffusion model for organic semiconductor devices with GaussFermi statistics and positive temperature feedback for the charge carrier mobilities. We apply temperature dependent Ohmic contact boundary conditions for the electrostatic potential and discretize the system by a finite volume based generalized ScharfetterGummel scheme. Using pathfollowing techniques we demonstrate that the model exhibits Sshaped currentvoltage curves with regions of negative differential resistance, which were only recently observed experimentally. 
S. Frigeri, M. Grasselli, J. Sprekels, Optimal distributed control of twodimensional nonlocal CahnHilliardNavierStokes systems with degenerate mobility and singular potential, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, 81 (2020), pp. 889931 (published online on 24.09.2018), DOI 10.1007/s0024501895247 .
Abstract
In this paper, we consider a twodimensional diffuse interface model for the phase separation of an incompressible and isothermal binary fluid mixture with matched densities. This model consists of the NavierStokes equations, nonlinearly coupled with a convective nonlocal CahnHilliard equation. The system rules the evolution of the volumeaveraged velocity of the mixture and the (relative) concentration difference of the two phases. The aim of this work is to study an optimal control problem for such a system, the control being a timedependent external force acting on the fluid. We first prove the existence of an optimal control for a given tracking type cost functional. Then we study the differentiability properties of the controltostate map, and we establish firstorder necessary optimality conditions. These results generalize the ones obtained by the first and the third authors jointly with E. Rocca in [19]. There the authors assumed a constant mobility and a regular potential with polynomially controlled growth. Here, we analyze the physically more relevant case of a degenerate mobility and a singular (e.g., logarithmic) potential. This is made possible by the existence of a unique strong solution which was recently proved by the authors and C. G. Gal in [14]. 
H. Meinlschmidt, Ch. Meyer, J. Rehberg, Regularization for optimal control problems associated to nonlinear evolution equations, Journal of Convex Analysis, 27 (2020), pp. 443485, DOI 10.20347/WIAS.PREPRINT.2576 .
Abstract
It is wellknown that in the case of a sufficiently nonlinear general optimal control problem there is very frequently the necessity for a compactness argument in order to pass to the limit in the state equation in the standard “calculus of variations” proof for the existence of optimal controls. For timedependent state equations, i.e., evolution equations, this is in particular unfortunate due to the difficult structure of compact sets in Bochnertype spaces. In this paper, we propose an abstract function space and a suitable regularization or Tychonov term for the objective functional which allows for the usual standard reasoning in the proof of existence of optimal controls and which admits a reasonably favorable structure in the characterization of optimal solutions via first order necessary conditions in, generally, the form of a variational inequality of obstacletype in time. We establish the necessary properties of the function space and the Tychonov term and derive the aforementioned variational inequality. The variational inequality can then be reformulated as a projection identity for the optimal control under additional assumptions. We give sufficient conditions on when these are satisfied. The considerations are complemented with a series of practical examples of possible constellations and choices in dependence on the varying control spaces required for the evolution equations at hand. 
H. Neidhardt, A. Stephan, V.A. Zagrebnov, Convergence rate estimates for Trotter product approximations of solution operators for nonautonomous Cauchy problems, Publications of the Research Institute for Mathematical Sciences, 56 (2020), pp. 83135 (published online 21.01.2020), DOI 10.4171/PRIMS/5615 .
Abstract
In the present paper we advocate the HowlandEvans approach to solution of the abstract nonautonomous Cauchy problem (nonACP) in a separable Banach space X. The main idea is to reformulate this problem as an autonomous Cauchy problem (ACP) in a new Banach space Lp(J,X), consisting of Xvalued functions on the timeinterval J. The fundamental observation is a onetoone correspondence between solution operators (propagators) for a nonACP and the corresponding evolution semigroups for ACP in Lp(J,X). We show that the latter also allows to apply a full power of the operatortheoretical methods to scrutinise the nonACP including the proof of the Trotter product approximation formulae with operatornorm estimate of the rate of convergence. The paper extends and improves some recent results in this direction in particular for Hilbert spaces. 
O. Souček, M. Heida, J. Málek, On a thermodynamic framework for developing boundary conditions for Korteweg fluids, International Journal of Engineering Science, 154 (2020), (published online on 20 June 2020), DOI https://doi.org/10.1016/j.ijengsci.2020.103316 .
Abstract
We provide a derivation of several classes of boundary conditions for fluids of Kortewegtype using a simple and transparent thermodynamic approach that automatically guarentees that the derived boundary conditions are compatible with the second law of thermodynamics. The starting assumption of our approach is to describe the boundary of the domain as the membrane separating two different continua, one inside the domain, and the other outside the domain. With this viewpoint one may employ the framework of continuum thermodynamics involving singular surfaces. This approach allows us to identify, for various classes of surface Helmholtz free energies, the corresponding surface entropy production mechanisms. By establishing the constitutive relations that guarantee that the surface entropy production is nonnegative, we identify a new class of boundary conditions, which on one hand generalizes in a nontrivial manner the Navier's slip boundary conditions, and on the other hand describes dynamic and static contact angle conditions. We explore the general model in detail for a particular case of Korteweg fluid where the Helmholtz free energy in the bulk is that of a van der Waals fluid. We perform a series of numerical experiments to document the basic qualitative features of the novel boundary conditions and their practical applicability to model phenomena such as the contact angle hysteresis. 
K. Disser, J. Rehberg, The 3D transient semiconductor equations with gradientdependent and interfacial recombination, Mathematical Models & Methods in Applied Sciences, 29 (2019), pp. 18191851, DOI 10.1142/S0218202519500350 .
Abstract
We establish the wellposedness of the transient van Roosbroeck system in three space dimensions under realistic assumptions on the data: nonsmooth domains, discontinuous coefficient functions and mixed boundary conditions. Moreover, within this analysis, recombination terms may be concentrated on surfaces and interfaces and may not only depend on chargecarrier densities, but also on the electric field and currents. In particular, this includes Avalanche recombination. The proofs are based on recent abstract results on maximal parabolic and optimal elliptic regularity of divergenceform operators. 
D.H. Doan, A. Glitzky, M. Liero, Analysis of a driftdiffusion model for organic semiconductor devices, Zeitschrift fur Angewandte Mathematik und Physik. ZAMP. Journal of Applied Mathematics and Physics. Journal de Mathematiques et de Physique Appliquees, 70 (2019), pp. 55/155/18, DOI 10.1007/s000330191089z .
Abstract
We discuss driftdiffusion models for chargecarrier transport in organic semiconductor devices. The crucial feature in organic materials is the energetic disorder due to random alignment of molecules and the hopping transport of carriers between adjacent energetic sites. The former leads to socalled GaussFermi statistics, which describe the occupation of energy levels by electrons and holes. The latter gives rise to complicated mobility models with a strongly nonlinear dependence on temperature, density of carriers, and electric field strength. We present the stateoftheart modeling of the transport processes and provide a first existence result for the stationary driftdiffusion model taking all of the peculiarities of organic materials into account. The existence proof is based on Schauder's fixedpoint theorem. 
M. Heida, S. Nesenenko, Stochastic homogenization of ratedependent models of monotone type in plasticity, Asymptotic Analysis, 112 (2019), pp. 185212, DOI 10.3233/ASY181502 .
Abstract
In this work we deal with the stochastic homogenization of the initial boundary value problems of monotone type. The models of monotone type under consideration describe the deformation behaviour of inelastic materials with a microstructure which can be characterised by random measures. Based on the Fitzpatrick function concept we reduce the study of the asymptotic behaviour of monotone operators associated with our models to the problem of the stochastic homogenization of convex functionals within an ergodic and stationary setting. The concept of Fitzpatrick's function helps us to introduce and show the existence of the weak solutions for ratedependent systems. The derivations of the homogenization results presented in this work are based on the stochastic twoscale convergence in Sobolev spaces. For completeness, we also present some twoscale homogenization results for convex functionals, which are related to the classical Gammaconvergence theory. 
G. Nika, B. Vernescu, Multiscale modeling of magnetorheological suspensions, ZAMP Zeitschrift fur Angewandte Mathematik und Physik. ZAMP. Journal of Applied Mathematics and Physics. Journal de Mathematiques et de Physique Appliquees, 71 (2020), pp. 14/114/19 (published online on 23.12.2019), DOI 10.1007/s0003301912384 .
Abstract
We develop a multiscale approach to describe the behavior of a suspension of solid magnetizable particles in a viscous nonconducting fluid in the presence of an externally applied magnetic field. By upscaling the quasistatic Maxwell equations coupled with the Stokes' equations we are able to capture the magnetorheological effect. The model we obtain generalizes the one introduced by Neuringer & Rosensweig for quasistatic phenomena. We derive the macroscopic constitutive properties explicitly in terms of the solutions of local problems. The effective coefficients have a nonlinear dependence on the volume fraction when chain structures are present. The velocity profiles computed for some simple flows, exhibit an apparent yield stress and the flowprofile resembles a Bingham fluid flow. 
D. Peschka, S. Haefner, L. Marquant, K. Jacobs, A. Münch, B. Wagner, Signatures of slip in dewetting polymer films, Proceedings of the National Academy of Sciences of the United States of America, 116 (2019), pp. 92759284, DOI 10.1073/pnas.1820487116 .

A. Stephan, H. Stephan, Memory equations as reduced Markov processes, Discrete and Continuous Dynamical Systems, 39 (2019), pp. 21332155, DOI 10.3934/dcds.2019089 .
Abstract
A large class of linear memory differential equations in one dimension, where the evolution depends on the whole history, can be equivalently described as a projection of a Markov process living in a higher dimensional space. Starting with such a memory equation, we give an explicit construction of the corresponding Markov process. From a physical point of view the Markov process can be understood as the change of the type of some quasiparticles along oneway loops. Typically, the arising Markov process does not have the detailed balance property. The method leads to a more realisitc modeling of memory equations. Moreover, it carries over the large number of investigation tools for Markov processes to memory equations, like the calculation of the equilibrium state, the asymptotic behavior and so on. The method can be used for an approximative solution of some degenerate memory equations like delay differential equations. 
F. Flegel, M. Heida, M. Slowik, Homogenization theory for the random conductance model with degenerate ergodic weights and unboundedrange jumps, Annales de l'Institut Henri Poincare. Probabilites et Statistiques, 55 (2019), pp. 12261257, DOI 10.1214/18AIHP917 .
Abstract
We study homogenization properties of the discrete Laplace operator with random conductances on a large domain in Zd. More precisely, we prove almostsure homogenization of the discrete Poisson equation and of the top of the Dirichlet spectrum. We assume that the conductances are stationary, ergodic and nearestneighbor conductances are positive. In contrast to earlier results, we do not require uniform ellipticity but certain integrability conditions on the lower and upper tails of the conductances. We further allow jumps of arbitrary length. Without the longrange connections, the integrability condition on the lower tail is optimal for spectral homogenization. It coincides with a necessary condition for the validity of a local central limit theorem for the random walk among random conductances. As an application of spectral homogenization, we prove a quenched large deviation principle for thenormalized and rescaled local times of the random walk in a growing box. Our proofs are based on a compactness result for the Laplacian's Dirichlet energy, Poincaré inequalities, Moser iteration and twoscale convergence 
F. Flegel, M. Heida, The fractional pLaplacian emerging from homogenization of the random conductance model with degenerate ergodic weights and unboundedrange jumps, Calculus of Variations and Partial Differential Equations, 59 (2020), pp. 8/18/39 (published online on 28.11.2019), DOI 10.1007/s0052601916634 .
Abstract
We study a general class of discrete pLaplace operators in the random conductance model with longrange jumps and ergodic weights. Using a variational formulation of the problem, we show that under the assumption of bounded first moments and a suitable lower moment condition on the weights, the homogenized limit operator is a fractional pLaplace operator. Under strengthened lower moment conditions, we can apply our insights also to the spectral homogenization of the discrete Lapalace operator to the continuous fractional Laplace operator. 
Y. Zheng, A. Fischer, M. Sawatzki, D.H. Doan, M. Liero, A. Glitzky, S. Reineke, S.C.B. Mannsfeld, Introducing pinMOS memory: A novel, nonvolatile organic memory device, Advanced Functional Materials, 30 (2020), pp. 1907119/11907119/10 (published online on 07.11.2019), DOI 10.1002/adfm.201907119 .
Abstract
In recent decades, organic memory devices have been researched intensely and they can, among other application scenarios, play an important role in the vision of an internet of things. Most studies concentrate on storing charges in electronic traps or nanoparticles while memory types where the information is stored in the local charge up of an integrated capacitance and presented by capacitance received far less attention. Here, a new type of programmable organic capacitive memory called pinmetaloxidesemiconductor (pinMOS) memory is demonstrated with the possibility to store multiple states. Another attractive property is that this simple, diodebased pinMOS memory can be written as well as read electrically and optically. The pinMOS memory device shows excellent repeatability, an endurance of more than 104 writereaderaseread cycles, and currently already over 24 h retention time. The working mechanism of the pinMOS memory under dynamic and steadystate operations is investigated to identify further optimization steps. The results reveal that the pinMOS memory principle is promising as a reliable capacitive memory device for future applications in electronic and photonic circuits like in neuromorphic computing or visual memory systems. 
L. Adam, M. Hintermüller, D. Peschka, Th.M. Surowiec, Optimization of a multiphysics problem in semiconductor laser design, SIAM Journal on Applied Mathematics, 79 (2019), pp. 257283, DOI 10.1137/18M1179183 .
Abstract
A multimaterial topology optimization framework is suggested for the simultaneous optimization of mechanical and optical properties to be used in the development of optoelectronic devices. Based on the physical aspects of the underlying device, a nonlinear multiphysics model for the elastic and optical properties is proposed. Rigorous proofs are provided for the sensitivity of the fundamental mode of the device with respect to the changes in the underlying topology. After proving existence and optimality results, numerical experiments leading to an optimal material distribution for maximizing the strain in a GeonSi microbridge are given. The highly favorable electronic properties of this design are demonstrated by steadystate simulations of the corresponding van Roosbroeck (driftdiffusion) system. 
F. Agnelli, A. Constantinescu, G. Nika, Design and testing of 3Dprinted microarchitectured polymer materials exhibiting a negative Poisson's ratio, Continuum Mechanics and Thermodynamics, 32 (2020), pp. 433449 (published online on 20.11.2019), DOI 10.1007/s00161019008516 .
Abstract
This work proposes the complete design cycle for several auxetic materials where the cycle consists of three steps (i) the design of the microarchitecture, (ii) the manufacturing of the material and (iii) the testing of the material. We use topology optimization via a levelset method and asymptotic homogenization to obtain periodic microarchitectured materials with a prescribed effective elasticity tensor and Poisson's ratio. The space of admissible microarchitectural shapes that carries orthotropic material symmetry allows to attain shapes with an effective Poisson's ratio below 1. Moreover, the specimens were manufactured using a commercial stereolithography Ember printer and are mechanically tested. The observed displacement and strain fields during tensile testing obtained by digital image correlation match the predictions from the finite element simulations and demonstrate the efficiency of the design cycle. 
A. Bacho, E. Emmrich, A. Mielke, An existence result and evolutionary Gammaconvergence for perturbed gradient systems, Journal of Evolution Equations, 19 (2019), pp. 479522, DOI 10.1007/s0002801900484x .
Abstract
We consider the initialvalue problem for the perturbed gradient flows, where a differential inclusion is formulated in terms of a subdifferential of an energy functional, a subdifferential of a dissipation potential and a more general perturbation, which is assumed to be continuous and to satisfy a suitable growth condition. Under additional assumptions on the dissipation potential and the energy functional, existence of strong solutions is shown by proving convergence of a semiimplicit discretization scheme with a variational approximation technique. 
P. Colli, G. Gilardi, J. Sprekels, A distributed control problem for a fractional tumor growth model, Mathematics  Open Access Journal, 7 (2019), pp. 792/1792/32, DOI 10.3390/math7090792 .
Abstract
In this paper, we study the distributed optimal control of a system of three evolutionary equations involving fractional powers of three selfadjoint, monotone, unbounded linear operators having compact resolvents. The system is a generalization of a CahnHilliard type phase field system modeling tumor growth that goes back to HawkinsDaarud et al. (Int. J. Numer. Math. Biomed. Eng. 28 (2012), 324.) The aim of the control process, which could be realized by either administering a drug or monitoring the nutrition, is to keep the tumor cell fraction under control while avoiding possible harm for the patient. In contrast to previous studies, in which the occurring unbounded operators governing the diffusional regimes were all given by the Laplacian with zero Neumann boundary conditions, the operators may in our case be different; more generally, we consider systems with fractional powers of the type that were studied in the recent work Adv. Math. Sci. Appl. 28 (2019), 343375 by the present authors. In our analysis, we show the Fréchet differentiability of the associated controltostate operator, establish the existence of solutions to the associated adjoint system, and derive the firstorder necessary conditions of optimality for a cost functional of tracking type. 
P. Colli, G. Gilardi, J. Sprekels, Deep quench approximation and optimal control of general CahnHilliard systems with fractional operators and double obstacle potentials, Discrete and Continuous Dynamical Systems  Series S, published online on 21.12.2019, urlhttps://doi.org/10.3934/dcdss.2020213, DOI 10.3934/dcdss.2020213 .
Abstract
In the recent paper ”Wellposedness and regularity for a generalized fractional CahnHilliard system”, the same authors derived general wellposedness and regularity results for a rather general system of evolutionary operator equations having the structure of a CahnHilliard system. The operators appearing in the system equations were fractional versions in the spectral sense of general linear operators A and B having compact resolvents and are densely defined, unbounded, selfadjoint, and monotone in a Hilbert space of functions defined in a smooth domain. The associated doublewell potentials driving the phase separation process modeled by the CahnHilliard system could be of a very general type that includes standard physically meaningful cases such as polynomial, logarithmic, and double obstacle nonlinearities. In the subsequent paper ”Optimal distributed control of a generalized fractional CahnHilliard system” (Appl. Math. Optim. (2018), https://doi.org/10.1007/s0024501895407) by the same authors, an analysis of distributed optimal control problems was performed for such evolutionary systems, where only the differentiable case of certain polynomial and logarithmic doublewell potentials could be admitted. Results concerning existence of optimizers and firstorder necessary optimality conditions were derived, where more restrictive conditions on the operators A and B had to be assumed in order to be able to show differentiability properties for the associated controltostate operator. In the present paper, we complement these results by studying a distributed control problem for such evolutionary systems in the case of nondifferentiable nonlinearities of double obstacle type. For such nonlinearities, it is well known that the standard constraint qualifications cannot be applied to construct appropriate Lagrange multipliers. To overcome this difficulty, we follow here the socalled ”deep quench” method. This technique, in which the nondifferentiable double obstacle nonlinearity is approximated by differentiable logarithmic nonlinearities, was first developed by P. Colli, M.H. FarshbafShaker and J. Sprekels in the paper ”A deep quench approach to the optimal control of an AllenCahn equation with dynamic boundary conditions and double obstacles” (Appl. Math. Optim. 71 (2015), pp. 124) and has proved to be a powerful tool in a number of optimal control problems with double obstacle potentials in the framework of systems of CahnHilliard type. We first give a general convergence analysis of the deep quench approximation that includes an error estimate and then demonstrate that its use leads in the double obstacle case to appropriate firstorder necessary optimality conditions in terms of a variational inequality and the associated adjoint state system. 
P. Colli, G. Gilardi, J. Sprekels, Optimal velocity control of a convective CahnHilliard system with double obstacles and dynamic boundary conditions: A `deep quench' approach, Journal of Convex Analysis, 26 (2019), pp. 485514.
Abstract
In this paper, we investigate a distributed optimal control problem for a convective viscous CahnHilliard system with dynamic boundary conditions. Such systems govern phase separation processes between two phases taking place in an incompressible fluid in a container and, at the same time, on the container boundary. The cost functional is of standard tracking type, while the control is exerted by the velocity of the fluid in the bulk. In this way, the coupling between the state (given by the associated order parameter and chemical potential) and control variables in the governing system of nonlinear partial differential equations is bilinear, which presents a difficulty for the analysis. In contrast to the previous paper Optimal velocity control of a viscous CahnHilliard system with convection and dynamic boundary conditions by the same authors, the bulk and surface free energies are of double obstacle type, which renders the state constraint nondifferentiable. It is well known that for such cases standard constraint qualifications are not satisfied so that standard methods do not apply to yield the existence of Lagrange multipliers. In this paper, we overcome this difficulty by taking advantage of results established in the quoted paper for logarithmic nonlinearities, using a socalled `deep quench approximation'. We derive results concerning the existence of optimal controls and the firstorder necessary optimality conditions in terms of a variational inequality and the associated adjoint system. 
P. Colli, G. Gilardi, J. Sprekels, Recent results on wellposedness and optimal control for a class of generalized fractional CahnHilliard systems, Control and Cybernetics, 48 (2019), pp. 153197.

P. Colli, G. Gilardi, J. Sprekels, Wellposedness and regularity for a fractional tumor growth model, Advances in Mathematical Sciences and Applications, 28 (2019), pp. 343375.
Abstract
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P. Colli, G. Gilardi, J. Sprekels, Wellposedness and regularity for a generalized fractional CahnHilliard system, Rendiconti Lincei  Matematica e Applicazioni, 30 (2019), pp. 437478.
Abstract
In this paper, we investigate a rather general system of two operator equations that has the structure of a viscous or nonviscous CahnHilliard system in which nonlinearities of doublewell type occur. Standard cases like regular or logarithmic potentials, as well as nondifferentiable potentials involving indicator functions, are admitted. The operators appearing in the system equations are fractional versions of general linear operators A and B, where the latter are densely defined, unbounded, selfadjoint and monotone in a Hilbert space of functions defined in a smooth domain and have compact resolvents. In this connection, we remark the fact that our definition of the fractional power of operators uses the approach via spectral theory. Typical cases are given by standard secondorder elliptic differential operators (e.g., the Laplacian) with zero Dirichlet or Neumann boundary conditions, but also other cases like fourthorder systems or systems involving the Stokes operator are covered by the theory. We derive in this paper general wellposedness and regularity results that extend corresponding results which are known for either the nonfractional Laplacian with zero Neumann boundary condition or the fractional Laplacian with zero Dirichlet condition. These results are entirely new if at least one of the operators A and B differs from the Laplacian. It turns out that the first eigenvalue λ_{1} of A plays an important und not entirely obvious role: if λ_{1} is positive, then the operators A and B may be completely unrelated; if, however, λ_{1} equals zero, then it must be simple and the corresponding onedimensional eigenspace has to consist of the constant functions and to be a subset of the domain of definition of a certain fractional power of B. We are able to show general existence, uniqueness, and regularity results for both these cases, as well as for both the viscous and the nonviscous system. 
P. Colli, A. Signori, J. Sprekels, Optimal control of a phase field system modelling tumor growth with chemotaxis and singular potentials, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, pp. published online on 21.10.2019, urlhttps://doi.org/10.1007/s00245019096186, DOI 10.1007/s00245019096186 .
Abstract
A distributed optimal control problem for an extended model of phase field type for tumor growth is addressed. In this model, the chemotaxis effects are also taken into account. The control is realized by two control variables that design the dispensation of some drugs to the patient. The cost functional is of tracking type, whereas the potential setting has been kept quite general in order to allow regular and singular potentials to be considered. In this direction, some relaxation terms have been introduced in the system. We show the wellposedness of the state system, the Fréchet differentiability of the controltostate operator in a suitable functional analytic framework, and, lastly, we characterize the firstorder necessary conditions of optimality in terms of a variational inequality involving the adjoint variables. 
P. Dondl, Th. Frenzel, A. Mielke, A gradient system with a wiggly energy and relaxed EDPconvergence, ESAIM. Control, Optimisation and Calculus of Variations, 25 (2019), pp. 68/168/45, DOI 10.1051/cocv/2018058 .
Abstract
If gradient systems depend on a microstructure, we want to derive a macroscopic gradient structure describing the effective behavior of the microscopic system. We introduce a notion of evolutionary Gammaconvergence that relates the microscopic energy and the microscopic dissipation potential with their macroscopic limits via Gammaconvergence. We call this notion relaxed EDPconvergence since the special structure of the dissipation functional may not be preserved under Gammaconvergence. However, by investigating the kinetic relation we derive the macroscopic dissipation potential. 
S.P. Frigeri, C.G. Gal, M. Grasselli, J. Sprekels, Strong solutions to nonlocal 2D CahnHilliardNavierStokes systems with nonconstant viscosity, degenerate mobility and singular potential, Nonlinearity, 32 (2019), pp. 678727, DOI 10.1088/13616544/aaedd0 .
Abstract
We consider a nonlinear system which consists of the incompressible NavierStokes equations coupled with a convective nonlocal CahnHilliard equation. This is a diffuse interface model which describes the motion of an incompressible isothermal mixture of two (partially) immiscible fluids having the same density. We suppose that the viscosity depends smoothly on the order parameter as well as the mobility. Moreover, we assume that the mobility is degenerate at the pure phases and that the potential is singular (e.g. of logarithmic type). This system is endowed with noslip boundary condition for the (average) velocity and homogeneous Neumann boundary condition for the chemical potential. Thus the total mass is conserved. In the twodimensional case, this problem was already analyzed in some joint papers of the first three authors. However, in the present general case, only the existence of a global weak solution, the (conditional) weakstrong uniqueness and the existence of the global attractor were proven. Here we are able to establish the existence of a (unique) strong solution through an approximation procedure based on time discretization. As a consequence, we can prove suitable uniform estimates which allow us to show some smoothness of the global attractor. Finally, we discuss the existence of strong solutions for the convective nonlocal CahnHilliard equation, with a given velocity field, in the three dimensional case as well. 
G. Gilardi, J. Sprekels, Asymptotic limits and optimal control for the CahnHilliard system with convection and dynamic boundary conditions, Nonlinear Analysis. An International Mathematical Journal, 178 (2019), pp. 131, DOI 10.1016/j.na.2018.07.007 .
Abstract
In this paper, we study initialboundary value problems for the CahnHilliard system with convection and nonconvex potential, where dynamic boundary conditions are assumed for both the associated order parameter and the corresponding chemical potential. While recent works addressed the case of viscous CahnHilliard systems, the `pure' nonviscous case is investigated here. In its first part, the paper deals with the asymptotic behavior of the solutions as time approaches infinity. It is shown that the $omega$limit of any trajectory can be characterized in terms of stationary solutions, provided the initial data are sufficiently smooth. The second part of the paper deals with the optimal control of the system by the fluid velocity. Results concerning existence and firstorder necessary optimality conditions are proved. Here, we have to restrict ourselves to the case of everywhere defined smooth potentials. In both parts of the paper, we start from corresponding known results for the viscous case, derive sufficiently strong estimates that are uniform with respect to the (positive) viscosity parameter, and then let the viscosity tend to zero to establish the sought results for the nonviscous case. 
L. Heltai, N. Rotundo, Error estimates in weighted Sobolev norms for finite element immersed interface methods, Computers & Mathematics with Applications. An International Journal, 78 (2019), pp. 35863604, DOI 10.1016/j.camwa.2019.05.029 .
Abstract
When solving elliptic partial differential equations in a region containing immersed interfaces (possibly evolving in time), it is often desirable to approximate the problem using an independent background discretisation, not aligned with the interface itself. Optimal convergence rates are possible if the discretisation scheme is enriched by allowing the discrete solution to have jumps aligned with the surface, at the cost of a higher complexity in the implementation. A much simpler way to reformulate immersed interface problems consists in replacing the interface by a singular force field that produces the desired interface conditions, as done in immersed boundary methods. These methods are known to have inferior convergence properties, depending on the global regularity of the solution across the interface, when compared to enriched methods. In this work we prove that this detrimental effect on the convergence properties of the approximate solution is only a local phenomenon, restricted to a small neighbourhood of the interface. In particular we show that optimal approximations can be constructed in a natural and inexpensive way, simply by reformulating the problem in a distributionally consistent way, and by resorting to weighted norms when computing the global error of the approximation. 
J. Lähnemann, M.O. Hill, J. Herranz, O. Marquardt, G. Gao, A. Al Hassan, A. Davtyan, S.O. Hruszkewycz, M.V. Holt, Ch. Huang, I. CalvoAlmazán, U. Jahn, U. Pietsch, L.J. Lauhon, L. Geelhaar, Correlated nanoscale analysis of the emission from wurtzite versus zincblende (In,Ga)As/GaAs nanowire coreshell quantum wells, ACS Nano, 19 (2019), pp. 44484457, DOI 10.1021/acs.nanolett.9b01241 .
Abstract
While the properties of wurtzite GaAs have been extensively studied during the past decade, little is known about the influence of the crystal polytype on ternary (In,Ga)As quantum well structures. We address this question with a unique combination of correlated, spatially resolved measurement techniques on coreshell nanowires that contain extended segments of both the zincblende and wurtzite polytypes. Cathodoluminescence hyperspectral imaging reveals a blueshift of the quantum well emission energy by 75 ± 15 meV in the wurtzite polytype segment. Nanoprobe Xray diffraction and atom probe tomography enable k•p calculations for the specific sample geometry to reveal two comparable contributions to this shift. First, there is a 30% drop in In mole fraction going from the zincblende to the wurtzite segment. Second, the quantum well is under compressive strain, which has a much stronger impact on the hole ground state in the wurtzite than in the zincblende segment. Our results highlight the role of the crystal structure in tuning the emission of (In,Ga)As quantum wells and pave the way to exploit the possibilities of threedimensional band gap engineering in coreshell nanowire heterostructures. At the same time, we have demonstrated an advanced characterization toolkit for the investigation of semiconductor nanostructures. 
V. Laschos, A. Mielke, Geometric properties of cones with applications on the HellingerKantorovich space, and a new distance on the space of probability measures, Journal of Functional Analysis, 276 (2019), pp. 35293576, DOI 10.1016/j.jfa.2018.12.013 .
Abstract
By studying general geometric properties of cone spaces, we prove the existence of a distance on the space of Probability measures that turns the HellingerKantorovich space into a cone space over the space of probabilities measures. Here we exploit a natural twoparameter scaling property of the HellingerKantorovich distance. For the new space, we obtain a full characterization of the geodesics. We also provide new geometric properties for the original space, including a twoparameter rescaling and reparametrization of the geodesics, localangle condition and some partial Ksemiconcavity of the squared distance, that it will be used in a future paper to prove existence of gradient flows. 
P. Nestler, N. Schlömer, O. Klein, J. Sprekels, F. Tröltzsch, Optimal control of semiconductor melts by traveling magnetic fields, Vietnam Journal of Mathematics, 47 (2019), pp. 793812, DOI 10.1007/s10013019003555 .
Abstract
In this paper, the optimal control of traveling magnetic fields in a process of crystal growth from the melt of semiconductor materials is considered. As controls, the phase shifts of the voltage in the coils of a heatermagnet module are employed to generate Lorentz forces for stirring the crystal melt in an optimal way. By the use of a new industrial heatermagnet module, the Lorentz forces have a stronger impact on the melt than in earlier technologies. It is known from experiments that during the growth process temperature oscillations with respect to time occur in the neighborhood of the solidliquid interface. These oscillations may strongly influence the quality of the growing single crystal. As it seems to be impossible to suppress them completely, the main goal of optimization has to be less ambitious, namely, one tries to achieve oscillations that have a small amplitude and a frequency which is sufficiently high such that the solidliquid interface does not have enough time to react to the oscillations. In our approach, we control the oscillations at a finite number of selected points in the neighborhood of the solidification front. The system dynamics is modeled by a coupled system of partial differential equations that account for instationary heat condution, turbulent melt flow, and magnetic field. We report on numerical methods for solving this system and for the optimization of the whole process. Different objective functionals are tested to reach the goal of optimization. 
J. Sprekels, H. Wu, Optimal distributed control of a CahnHilliardDarcy system with mass sources, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, pp. published online on 24.01.2019, urlhttps://doi.org/10.1007/s00245019095554, DOI 10.1007/s00245019095554 .
Abstract
In this paper, we study an optimal control problem for a twodimensional CahnHilliardDarcy system with mass sources that arises in the modeling of tumor growth. The aim is to monitor the tumor fraction in a finite time interval in such a way that both the tumor fraction, measured in terms of a tracking type cost functional, is kept under control and minimal harm is inflicted to the patient by administering the control, which could either be a drug or nutrition. We first prove that the optimal control problem admits a solution. Then we show that the controltostate operator is Fréchet differentiable between suitable Banach spaces and derive the firstorder necessary optimality conditions in terms of the adjoint variables and the usual variational inequality. 
A.F.M. TER Elst, J. Rehberg, Consistent operator semigroups and their interpolation, Journal of Operator Theory, 82 (2019), pp. 321, DOI 10.7900/jot.2017nov15.2233 .
Abstract
Under a mild regularity condition we prove that the generator of the interpolation of two C_{0}semigroups is the interpolation of the two generators. 
A. Glitzky, M. Liero, Instationary driftdiffusion problems with GaussFermi statistics and fielddependent mobility for organic semiconductor devices, Communications in Mathematical Sciences, 17 (2019), pp. 3359, DOI 10.4310/cms.2019.v17.n1.a2 .
Abstract
This paper deals with the analysis of an instationary driftdiffusion model for organic semiconductor devices including GaussFermi statistics and applicationspecific mobility functions. The charge transport in organic materials is realized by hopping of carriers between adjacent energetic sites and is described by complicated mobility laws with a strong nonlinear dependence on temperature, carrier densities and the electric field strength. To prove the existence of global weak solutions, we consider a problem with (for small densities) regularized state equations on any arbitrarily chosen finite time interval. We ensure its solvability by time discretization and passage to the timecontinuous limit. Positive lower a priori estimates for the densities of its solutions that are independent of the regularization level ensure the existence of solutions to the original problem. Furthermore, we derive for these solutions global positive lower and upper bounds strictly below the density of transport states for the densities. The estimates rely on Moser iteration techniques. 
P. Farrell, D. Peschka, Nonlinear diffusion, boundary layers and nonsmoothness: Analysis of challenges in driftdiffusion semiconductor simulations, Computers & Mathematics with Applications. An International Journal, 78 (2019), pp. 37313747, DOI 10.1016/j.camwa.2019.06.007 .
Abstract
We analyze and benchmark the error and the convergence order of finite difference, finiteelement as well as Voronoi finitevolume discretization schemes for the driftdiffusion equations describing charge transport in bulk semiconductor devices. Three common challenges, that can corrupt the precision of numerical solutions, will be discussed: boundary layers at Ohmic contacts, discontinuties in the doping profile, and corner singularities in Lshaped domains. The influence on the order of convergence is assessed for each computational challenge and the different discretization schemes. Additionally, we provide an analysis of the inner boundary layer asymptotics near Ohmic contacts to support our observations. 
M. Liero, S. Melchionna, The weighted energydissipation principle and evolutionary Gammaconvergence for doubly nonlinear problems, ESAIM. Control, Optimisation and Calculus of Variations, 25 (2019), pp. 36/136/38, DOI 10.1051/cocv/2018023 .
Abstract
We consider a family of doubly nonlinear evolution equations that is given by families of convex dissipation potentials, nonconvex energy functionals, and external forces parametrized by a small parameter ε. For each of these problems, we introduce the socalled weighted energydissipation (WED) functional, whose minimizer correspond to solutions of an ellipticintime regularization of the target problems with regularization parameter δ. We investigate the relation between the Γconvergence of the WED functionals and evolutionary Γconvergence of the associated systems. More precisely, we deal with the limits δ→0, ε→0, as well as δ+ ε→0 either in the sense of Γconvergence of functionals or in the sense of evolutionary Γconvergence of functionaldriven evolution problems, or both. Additionally, we provide some quantitative estimates on the rate of convergence for the limit ε→0, in the case of quadratic dissipation potentials and uniformly λconvex energy functionals. Finally, we discuss a homogenization problem as an example of application. 
M. Radziunas, J. Fuhrmann, A. Zeghuzi, H.J. Wünsche, Th. Koprucki, C. Brée, H. Wenzel, U. Bandelow, Efficient coupling of dynamic electrooptical and heattransport models for highpower broadarea semiconductor lasers, Optical and Quantum Electronics, 51 (2019), pp. 69/169/10, DOI 10.1007/s1108201917921 .
Abstract
In this work, we discuss the modeling of edgeemitting highpower broadarea semiconductor lasers. We demonstrate an efficient iterative coupling of a slow heat transport (HT) model defined on multiple verticallateral laser crosssections with a fast dynamic electrooptical (EO) model determined on the longitudinallateral domain that is a projection of the device to the active region of the laser. Whereas the HTsolver calculates temperature and thermallyinduced refractive index changes, the EOsolver exploits these distributions and provides timeaveraged field intensities, quasiFermi potentials, and carrier densities. All these timeaveraged distributions are used repetitively by the HTsolver for the generation of the heat sources entering the HT problem solved in the next iteration step.
Contributions to Collected Editions

C. Cancès, C. ChainaisHillairet, J. Fuhrmann, B. Gaudeul, On four numerical schemes for a unipolar degenerate driftdiffusion model, in: Proceedings of Finite Volumes for Complex Applications IX, Bergen, Norway, June 2020, R. Klöfkorn, F. Radu, E. Keijgavlen, J. Fuhrmann, eds., Springer Proceedings in Mathematics & Statistics, Springer International Publishing, Cham et al., 2020, pp. 163171, DOI 10.1007/9783030436513_13 .

U.W. Pohl, A. Strittmatter, A. Schliwa, M. Lehmann, T. Niermann, T. Heindel, S. Reitzenstein, M. Kantner, U. Bandelow, Th. Koprucki, H.J. Wünsche, Stressorinduced site control of quantum dots for singlephoton sources, in: Semiconductor Nanophotonics, M. Kneissl, A. Knorr, S. Reitzenstein, A. Hoffmann, eds., 194 of Springer Series in SolidState Sciences, Springer, Cham, 2020, pp. published online on 11.03.2020, DOI 10.1007/9783030356569_3 .
Abstract
The strain field of selectively oxidized AlOx current apertures in an AlGaAs/GaAs mesa is utilized to define the nucleation site of InGaAs/GaAs quantum dots. A design is developed that allows for the selfaligned growth of single quantum dots in the center of a circular mesa. Measurements of the strain tensor applying transmissionelectron holography yield excellent agreement with the calculated strain field. Singledot spectroscopy of sitecontrolled dots proves narrow excitonic linewidth virtually free of spectral diffusion due to quantumdot growth in a defectfree matrix. Implementation of such dots in an electrically driven pin structure yields singledot electroluminescence. Singlephoton emission with excellent purity is proved for this device using a Hanbury Brown and Twiss setup. The injection efficiency of the initial pin design is affected by a substantial lateral current spreading close to the oxide aperture. Applying 3D carriertransport simulation a ppn doping profile is developed achieving a substantial improvement of the current injection. 
S. Rodt, P.I. Schneider, L. Zschiedrich, T. Heindel, S. Bounouar, M. Kantner, Th. Koprucki, U. Bandelow, S. Burger, S. Reitzenstein, Deterministic quantum devices for optical quantum communication, in: Semiconductor Nanophotonics, M. Kneissl, A. Knorr, S. Reitzenstein, A. Hoffmann, eds., 194 of Springer Series in SolidState Sciences, Springer, Cham, 2020, pp. published online on 11.03.2020, DOI 10.1007/9783030356569 .
Abstract
Photonic quantum technologies are based on the exchange of information via single photons. The information is typically encoded in the polarization of the photons and security is ensured intrinsically via principles of quantum mechanics such as the nocloning theorem. Thus, all optical quantum communication networks rely crucially on the availability of suitable quantumlight sources. Such light sources with close to ideal optical and quantum optical properties can be realized by selfassembled semiconductor quantum dots. These highquality nanocrystals are predestined singlephoton emitters due to their quasi zerodimensional carrier confinement. Still, the development of practical quantumdotbased sources of single photons and entangledphoton pairs for applications in photonic quantum technology and especially for the quantumrepeater scheme is very demanding and requires highly advanced device concepts and deterministic fabrication technologies. This is mainly explained by their random position and emission energy as well as by the low photonextraction efficiency in simple planar device configurations. 
S. Schulz, D. Chaudhuri, M. O'Donovan, S. Patra, T. Streckenbach, P. Farrell, O. Marquardt, Th. Koprucki, Multiscale modeling of electronic, optical, and transport properties of IIIN alloys and heterostructures, in: Proceedings Physics and Simulation of Optoelectronic Devices XXVIII, 11274, San Francisco, California, USA, 2020, pp. 416426, DOI 10.1117/12.2551055 .

J. Fuhrmann, D.H. Doan, A. Glitzky, M. Liero, G. Nika, Unipolar driftdiffusion simulation of Sshaped currentvoltage relations for organic semiconductor devices, in: Proceedings of ``Finite Volumes for Complex Applications IX'', R. Klöfkorn, E. Keilegavlen, F.A. Radu, J. Fuhrmann, eds., 323 of Springer Proceedings in Mathematics & Statistics, Springer, Cham, 2020, pp. 625633, DOI 10.1007/9783030436513_59 .
Abstract
We discretize a unipolar electrothermal driftdiffusion model for organic semiconductor devices with GaussFermi statistics and charge carrier mobilities having positive temperature feedback. We apply temperature dependent Ohmic contact boundary conditions for the electrostatic potential and use a finite volume based generalized ScharfetterGummel scheme. Applying pathfollowing techniques we demonstrate that the model exhibits Sshaped currentvoltage curves with regions of negative differential resistance, only recently observed experimentally. 
M. Kantner, Th. Höhne, Th. Koprucki, S. Burger, H.J. Wünsche, F. Schmidt, A. Mielke, U. Bandelow, Multidimensional modeling and simulation of semiconductor nanophotonic devices, in: Semiconductor Nanophotonics, M. Kneissl, A. Knorr, S. Reitzenstein, A. Hoffmann, eds., 194 of Springer Series in SolidState Sciences, Springer, Cham, 2020, pp. published online on 11.03.2020, DOI 10.1007/9783030356569_7 .
Abstract
Selfconsistent modeling and multidimensional simulation of semiconductor nanophotonic devices is an important tool in the development of future integrated light sources and quantum devices. Simulations can guide important technological decisions by revealing performance bottlenecks in new device concepts, contribute to their understanding and help to theoretically explore their optimization potential. The efficient implementation of multidimensional numerical simulations for computeraided design tasks requires sophisticated numerical methods and modeling techniques. We review recent advances in devicescale modeling of quantum dot based singlephoton sources and laser diodes by selfconsistently coupling the optical Maxwell equations with semiclassical carrier transport models using semiclassical and fully quantum mechanical descriptions of the optically active region, respectively. For the simulation of realistic devices with complex, multidimensional geometries, we have developed a novel hpadaptive finite element approach for the optical Maxwell equations, using mixed meshes adapted to the multiscale properties of the photonic structures. For electrically driven devices, we introduced novel discretization and parameterembedding techniques to solve the driftdiffusion system for strongly degenerate semiconductors at cryogenic temperatures. Our methodical advances are demonstrated on various applications, including verticalcavity surfaceemitting lasers, grating couplers and singlephoton sources. 
M. Kantner, Th. Koprucki, Nonisothermal ScharfetterGummel scheme for electrothermal transport simulation in degenerate semiconductors, in: Proceedings of ``Finite Volumes for Complex Applications IX'', R. Klöfkorn, E. Keilegavlen, F.A. Radu, J. Fuhrmann, eds., 323 of Springer Proceedings in Mathematics & Statistics, Springer, Cham, 2020, pp. 173182, DOI 10.1007/9783030436513_14 .
Abstract
Electrothermal transport phenomena in semiconductors are described by the nonisothermal driftdiffusion system. The equations take a remarkably simple form when assuming the Kelvin formula for the thermopower. We present a novel, nonisothermal generalization of the ScharfetterGummel finite volume discretization for degenerate semiconductors obeying FermiDirac statistics, which preserves numerous structural properties of the continuous model on the discrete level. The approach is demonstrated by 2D simulations of a heterojunction bipolar transistor. 
M. Kantner, A. Mielke, M. Mittnenzweig, N. Rotundo, Mathematical modeling of semiconductors: From quantum mechanics to devices, in: Topics in Applied Analysis and Optimisation, M. Hintermüller, J.F. Rodrigues, eds., CIM Series in Mathematical Sciences, Springer Nature Switzerland AG, Cham, 2019, pp. 269293, DOI 10.1007/9783030331160 .
Abstract
We discuss recent progress in the mathematical modeling of semiconductor devices. The central result of this paper is a combined quantumclassical model that selfconsistently couples van Roosbroeck's driftdiffusion system for classical charge transport with a Lindbladtype quantum master equation. The coupling is shown to obey fundamental principles of nonequilibrium thermodynamics. The appealing thermodynamic properties are shown to arise from the underlying mathematical structure of a damped Hamitlonian system, which is an isothermal version of socalled GENERIC systems. The evolution is governed by a Hamiltonian part and a gradient part involving a Poisson operator and an Onsager operator as geoemtric structures, respectively. Both parts are driven by the conjugate forces given in terms of the derivatives of a suitable free energy. 
M. Kantner, Th. Koprucki, H.J. Wünsche, U. Bandelow, Simulation of quantum dot based singlephoton sources using the SchrödingerPoissonDriftDiffusionLindblad system, in: Proceedings of the 24th International Conference on Simulation of Semiconductor Processes and Devices (SISPAD 2019), F. Driussi, ed., 2019, pp. 355358, DOI 10.1007/9783030221160_11 .

D. Peschka, M. Thomas, T. Ahnert, A. Münch, B. Wagner, Gradient structures for flows of concentrated suspensions, in: Topics in Applied Analysis and Optimisation, M. Hintermüller, J.F. Rodrigues, eds., CIM Series in Mathematical Sciences, Springer Nature Switzerland AG, Cham, 2019, pp. 295318, DOI 10.1007/9783030331160 .
Abstract
In this work we investigate a twophase model for concentrated suspensions. We construct a PDE formulation using a gradient flow structure featuring dissipative coupling between fluid and solid phase as well as different driving forces. Our construction is based on the concept of flow maps that also allows it to account for flows in moving domains with free boundaries. The major difference compared to similar existing approaches is the incorporation of a nonsmooth twohomogeneous term to the dissipation potential, which creates a normal pressure even for pure shear flows. 
P. Colli, G. Gilardi, J. Sprekels, Nonlocal phase field models of viscous CahnHilliard type, in: Topics in Applied Analysis and Optimisation, M. Hintermüller, J.F. Rodrigues, eds., CIM Series in Mathematical Sciences, Springer Nature Switzerland AG, Cham, 2019, pp. 71100, DOI 10.1007/9783030331160 .
Abstract
A nonlocal phase field model of viscous CahnHilliard type is considered. This model constitutes a nonlocal version of a model for twospecies phase segregation on an atomic lattice under the presence of diffusion that has been studied in a series of papers by P. PodioGuidugli and the present authors. The resulting system of differential equations consists of a highly nonlinear parabolic equation coupled to a nonlocal ordinary differential equation, which has singular terms that render the analysis difficult. Some results are presented on the wellposedness and stability of the system as well as on the distributed optimal control problem. 
TH. Koprucki, A. Maltsi, T. Niermann, T. Streckenbach, K. Tabelow, J. Polzehl, On a database of simulated TEM images for In(Ga)As/GaAs quantum dots with various shapes, in: Proceedings of the 19th International Conference on Numerical Simulation of Optoelectronic Devices  NUSOD 2019, J. Piprek, K. Hinze, eds., IEEE Conference Publications Management Group, Piscataway, 2019, pp. 1314, DOI 10.1109/NUSOD.2019.8807025 .
Preprints, Reports, Technical Reports

D. Peschka, M. Rosenau, Twophase flows for sedimentation of suspensions, Preprint no. 2743, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2743 .
Abstract, PDF (12 MByte)
We present a twophase flow model that arises from energeticvariational arguments and study its implication for the sedimentation of buoyant particles in a viscous fluid inside a HeleShaw cell and also compare corresponding simulation results to experiments. Based on a minimal dissipation argument, we provide a simplified 1D model applicable to sedimentation and study its properties and the numerical discretization. We also explore different aspects of its numerical discretization in 2D. The focus is on different possible stabilization techniques and their impact on the qualitative behavior of solutions. We use experimental data to verify some first qualitative model predictions and discuss these experiments for different stages of batch sedimentation. 
M. Heida, Stochastic homogenization on randomly perforated domains, Preprint no. 2742, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2742 .
Abstract, PDF (1175 kByte)
We study the existence of uniformly bounded extension and trace operators for W^{1,p}functions on randomly perforated domains, where the geometry is assumed to be stationary ergodic. Such extension and trace operators are important for compactness in stochastic homogenization. In contrast to former approaches and results, we use very weak assumptions on the geometry which we call local (δ, M)regularity, isotropic cone mixing and bounded average connectivity. The first concept measures local Lipschitz regularity of the domain while the second measures the mesoscopic distribution of void space. The third is the most tricky part and measures the ”mesoscopic” connectivity of the geometry. In contrast to former approaches we do not require a minimal distance between the inclusions and we allow for globally unbounded Lipschitz constants and percolating holes. We will illustrate our method by applying it to the Boolean model based on a Poisson point process and to a Delaunay pipe process. We finally introduce suitable Sobolev spaces on R^{d} and Ω in order to construct a stochastic twoscale convergence method and apply the resulting theory to the homogenization of a pLaplace problem on a randomly perforated domain. 
P. Colli, G. Gilardi, J. Sprekels, An asymptotic analysis for a generalized CahnHilliard system with fractional operators, Preprint no. 2741, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2741 .
Abstract, PDF (311 kByte)
In a recent paper the same authors have proved existence, uniqueness and regularity results for a class of viscous and nonviscous CahnHilliard systems of two operator equations in which nonlinearities of doublewell type, like regular or logarithmic potentials, as well as nonsmooth potentials with indicator functions, were admitted. The operators appearing in the system equations are fractional powers in the spectral sense of general linear operators, which are densely defined, unbounded, selfadjoint, and monotone in the Hilbert space of squareintegrable functions on a bounded and smooth threedimensional domain, and have compact resolvents. Here, for the case of the viscous system, we analyze the asymptotic behavior of the solution as the fractional power coefficient of the second operator tends to zero. We prove convergence to a phase relaxation problem at the limit, and we also investigate this limiting problem, in which an additional term containing the projection of the phase variable on the kernel of the second operator appears. 
P. Colli, M.H. Farshbaf Shaker, K. Shirakawa, N. Yamazaki, Optimal control for shape memory alloys of the onedimensional Frémond model, Preprint no. 2737, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2737 .
Abstract, PDF (700 kByte)
In this paper, we consider optimal control problems for the onedimensional Frémond model for shape memory alloys. This model is constructed in terms of basic functionals like free energy and pseudopotential of dissipation. The state problem is expressed by a system of partial differential equations involving the balance equations for energy and momentum. We prove the existence of an optimal control that minimizes the cost functional for a nonlinear and nonsmooth state problem. Moreover, we show the necessary condition of the optimal pair by using optimal control problems for approximating systems. 
TH. Eiter, On the spatially asymptotic structure of timeperiodic solutions to the NavierStokes equations, Preprint no. 2727, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2727 .
Abstract, PDF (258 kByte)
The asymptotic behavior of weak timeperiodic solutions to the NavierStokes equations with a drift term in the threedimensional whole space is investigated. The velocity field is decomposed into a timeindependent and a remaining part, and separate asymptotic expansions are derived for both parts and their gradients. One observes that the behavior at spatial infinity is determined by the corresponding Oseen fundamental solutions. 
P. Colli, G. Gilardi, J. Sprekels, Optimal control of a phase field system of Caginalp type with fractional operators, Preprint no. 2725, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2725 .
Abstract, PDF (360 kByte)
In their recent work “Wellposedness, regularity and asymptotic analyses for a fractional phase field system” (Asymptot. Anal. 114 (2019), 93128), two of the present authors have studied phase field systems of Caginalp type, which model nonconserved, nonisothermal phase transitions and in which the occurring diffusional operators are given by fractional versions in the spectral sense of unbounded, monotone, selfadjoint, linear operators having compact resolvents. In this paper, we complement this analysis by investigating distributed optimal control problems for such systems. It is shown that the associated controltostate operator is Fréchet differentiable between suitable Banach spaces, and meaningful firstorder necessary optimality conditions are derived in terms of a variational inequality and the associated adjoint state variables. 
R. Chill, H. Meinlschmidt, J. Rehberg, On the numerical range of second order elliptic operators with mixed boundary conditions in L^{p}, Preprint no. 2723, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2723 .
Abstract, PDF (247 kByte)
We consider second order elliptic operators with real, nonsymmetric coefficient functions which are subject to mixed boundary conditions. The aim of this paper is to provide uniform resolvent estimates for the realizations of these operators on L^{p} in a most direct way and under minimal regularity assumptions on the domain. This is analogous to the main result in [7]. Ultracontractivity of the associated semigroups is also considered. All results are for two different form domains realizing mixed boundary conditions. We further consider the case of Robin instead of classical Neumann boundary conditions and also allow for operators inducing dynamic boundary conditions. The results are complemented by an intrinsic characterization of elements of the form domains inducing mixed boundary conditions. 
J. Sprekels, F. Tröltzsch, Sparse optimal control of a phase field system with singular potentials arising in the modeling of tumor growth, Preprint no. 2721, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2721 .
Abstract, PDF (326 kByte)
In this paper, we study an optimal control problem for a nonlinear system of reactiondiffusion equations that constitutes a simplified and relaxed version of a thermodynamically consistent phase field model for tumor growth originally introduced in [13]. The model takes the effect of chemotaxis into account but neglects velocity contributions. The unknown quantities of the governing state equations are the chemical potential, the (normalized) tumor fraction, and the nutrient extracellular water concentration. The equation governing the evolution of the tumor fraction is dominated by the variational derivative of a doublewell potential which may be of singular (e.g., logarithmic) type. In contrast to the recent paper [10] on the same system, we consider in this paper sparsity effects, which means that the cost functional contains a nondifferentiable (but convex) contribution like the L^{1}norm. For such problems, we derive firstorder necessary optimality conditions and conditions for directional sparsity, both with respect to space and time, where the latter case is of particular interest for practical medical applications in which the control variables are given by the administration of cytotoxic drugs or by the supply of nutrients. In addition to these results, we prove that the corresponding controltostate operator is twice continuously differentiable between suitable Banach spaces, using the implicit function theorem. This result, which complements and sharpens a differentiability result derived in [10], constitutes a prerequisite for a future derivation of secondorder sufficient optimality conditions. 
D. Bothe, P.É. Druet, Wellposedness analysis of multicomponent incompressible flow models, Preprint no. 2720, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2720 .
Abstract, PDF (465 kByte)
In this paper, we extend our study of mass transport in multicomponent isothermal fluids to the incompressible case. For a mixture, incompressibility is defined as the independence of average volume on pressure, and a weighted sum of the partial mass densities of the species stays constant. In this type of models, non solenoidal effects affect the velocity field in the NavierStokes equations and, due to different specific volumes of the species, the pressure remains connected to the densities by algebraic formula. By means of a change of variables in the transport problem, we equivalently reformulate the PDE system as to eliminate positivity and incompressibility constraints affecting the density, and prove two type of results: the localintime wellposedness in classes of strong solutions, and the globalintime existence of solutions for initial data sufficiently close to a smooth equilibrium solution. 
A. Glitzky, M. Liero, G. Nika, Dimension reduction of thermistor models for largearea organic lightemitting diodes, Preprint no. 2719, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2719 .
Abstract, PDF (328 kByte)
An effective system of partial differential equations describing the heat and current flow through a thin organic lightemitting diode (OLED) mounted on a glass substrate is rigorously derived from a recently introduced fully threedimensional φ(x)Laplace thermistor model. The OLED consists of several thin layers that scale differently with respect to the multiscale parameter ε > 0 which is the ratio between the total thickness and the lateral extent of the OLED. Starting point of the derivation is a rescaled formulation of the currentflow equation in the OLED for the driving potential and the heat equation in OLED and glass substrate with Joule heat term concentrated in the OLED. Assuming physically motivated scalings in the electrical flux functions, uniform a priori bounds are derived for the solutions of the threedimensional system which facilitates the extraction of converging subsequences with limits that are identified as solutions of a dimension reduced system. In the latter, the effective currentflow equation is given by two semilinear equations in the twodimensional crosssections of the electrodes and algebraic equations for the continuity of the electrical fluxes through the organic layers. The effective heat equation is formulated only in the glass substrate with Joule heat term on the part of the boundary where the OLED is mounted. 
A. Mielke, R.R. Netz, S. Zendehroud, A rigorous derivation and energetics of a wave equation with fractional damping, Preprint no. 2718, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2718 .
Abstract, PDF (312 kByte)
We consider a linear system that consists of a linear wave equation on a horizontal hypersurface and a parabolic equation in the half space below. The model describes longitudinal elastic waves in organic monolayers at the waterair interface, which is an experimental setup that is relevant for understanding wave propagation in biological membranes. We study the scaling regime where the relevant horizontal length scale is much larger than the vertical length scale and provide a rigorous limit leading to a fractionallydamped wave equation for the membrane. We provide the associated existence results via linear semigroup theory and show convergence of the solutions in the scaling limit. Moreover, based on the energydissipation structure for the full model, we derive a natural energy and a natural dissipation function for the fractionallydamped wave equation with a time derivative of order 3/2. 
E. Ipocoana, A. Zafferi, Further regularity and uniqueness results for a nonisothermal CahnHilliard equation, Preprint no. 2716, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2716 .
Abstract, PDF (270 kByte)
The aim of this paper is to establish new regularity results for a nonisothermal CahnHilliard system in the twodimensional setting. The main achievement is a crucial L^{∞} estimate for the temperature, obtained by a suitable Moser iteration scheme. Our results in particular allow us to get a new simplified version of the uniqueness proof for the considered model. 
J. Maas, A. Mielke, Modeling of chemical reaction systems with detailed balance using gradient structures, Preprint no. 2712, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2712 .
Abstract, PDF (552 kByte)
We consider various modeling levels for spatially homogeneous chemical reaction systems, namely the chemical master equation, the chemical Langevin dynamics, and the reactionrate equation. Throughout we restrict our study to the case where the microscopic system satisfies the detailedbalance condition. The latter allows us to enrich the systems with a gradient structure, i.e. the evolution is given by a gradientflow equation. We present the arising links between the associated gradient structures that are driven by the relative entropy of the detailedbalance steady state. The limit of large volumes is studied in the sense of evolutionary Γconvergence of gradient flows. Moreover, we use the gradient structures to derive hybrid models for coupling different modeling levels. 
S. Bartels, M. Milicevic, M. Thomas, N. Weber, Fully discrete approximation of rateindependent damage models with gradient regularization, Preprint no. 2707, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2707 .
Abstract, PDF (3444 kByte)
This work provides a convergence analysis of a timediscrete scheme coupled with a finiteelement approximation in space for a model for partial, rateindependent damage featuring a gradient regularization as well as a nonsmooth constraint to account for the unidirectionality of the damage evolution. The numerical algorithm to solve the coupled problem of quasistatic small strain linear elasticity with rateindependent gradient damage is based on a Variable ADMMmethod to approximate the nonsmooth contribution. Spacediscretization is based on P1 finite elements and the algorithm directly couples the timestep size with the spatial grid size h. For a wide class of gradient regularizations, which allows both for Sobolev functions of integrability exponent r ∈ (1, ∞) and for BVfunctions, it is shown that solutions obtained with the algorithm approximate as h → 0 a semistable energetic solution of the original problem. The latter is characterized by a minimality property for the displacements, a semistability inequality for the damage variable and an energy dissipation estimate. Numerical benchmark experiments confirm the stability of the method. 
H. Meinlschmidt, J. Rehberg, Extrapolated elliptic regularity and application to the van Roosbroeck system of semiconductor equations, Preprint no. 2705, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2705 .
Abstract, PDF (351 kByte)
In this paper we present a general extrapolated elliptic regularity result for second order differential operators in divergence form on fractional Sobolevtype spaces of negative order X^{s1,q}_{D}(Ω) for s > 0 small, including mixed boundary conditions and with a fully nonsmooth geometry of Ω and the Dirichlet boundary part D. We expect the result to find applications in the analysis of nonlinear parabolic equations, in particular for quasilinear problems or when treating coupled systems of equations. To demonstrate the usefulness of our result, we give a new proof of localintime existence and uniqueness for the van Roosbroeck system for semiconductor devices which is much simpler than already established proofs. 
P.É. Druet, A theory of generalised solutions for ideal gas mixtures with MaxwellStefan diffusion, Preprint no. 2700, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2700 .
Abstract, PDF (363 kByte)
After the pioneering work by Giovangigli on mathematics of multicomponent flows, several attempts were made to introduce global weak solutions for the PDEs describing the dynamics of fluid mixtures. While the incompressible case with constant density was enlighted well enough due to results by Chen and Jüngel (isothermal case), or Marion and Temam, some open questions remain for the weak solution theory of gas mixtures with their corresponding equations of mixed parabolichyperbolic type. For instance, Mucha, Pokorny and Zatorska showed the possibility to stabilise the hyperbolic component by means of the BreschDesjardins technique and a regularisation of pressure preventing vacuum. The result by Dreyer, Druet, Gajewski and Guhlke avoids emphex machina stabilisations, but the mathematical assumption that the Onsager matrix is uniformly positive on certain subspaces leads, in the dilute limit, to infinite diffusion velocities which are not compatible with the MaxwellStefan form of diffusion fluxes. In this paper, we prove the existence of global weak solutions for isothermal and ideal compressible mixtures with natural diffusion. The main new tool is an asymptotic condition imposed at low pressure on the binary MaxwellStefan diffusivities, which compensates possibly extreme behaviour of weak solutions in the rarefied regime. 
M. Heida, M. Kantner, A. Stephan, Consistency and convergence for a family of finite volume discretizations of the FokkerPlanck operator, Preprint no. 2684, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2684 .
Abstract, PDF (2376 kByte)
We introduce a family of various finite volume discretization schemes for the FokkerPlanck operator, which are characterized by different weight functions on the edges. This family particularly includes the wellestablished ScharfetterGummel discretization as well as the recently developed squareroot approximation (SQRA) scheme. We motivate this family of discretizations both from the numerical and the modeling point of view and provide a uniform consistency and error analysis. Our main results state that the convergence order primarily depends on the quality of the mesh and in second place on the quality of the weights. We show by numerical experiments that for small gradients the choice of the optimal representative of the discretization family is highly nontrivial while for large gradients the ScharfetterGummel scheme stands out compared to the others. 
A. Maltsi, T. Niermann, T. Streckenbach, K. Tabelow, Th. Koprucki, Numerical simulation of TEM images for In(Ga)As/GaAs quantum dots with various shapes, Preprint no. 2682, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2682 .
Abstract, PDF (7946 kByte)
We present a mathematical model and a tool chain for the numerical simulation of TEM images of semiconductor quantum dots (QDs). This includes elasticity theory to obtain the strain profile coupled with the DarwinHowieWhelan equations, describing the propagation of the electron wave through the sample. We perform a simulation study on indium gallium arsenide QDs with different shapes and compare the resulting TEM images to experimental ones. This tool chain can be applied to generate a database of simulated TEM images, which is a key element of a novel concept for modelbased geometry reconstruction of semiconductor QDs, involving machine learning techniques. 
G. Nika, B. Vernescu, Microgeometry effects on the nonlinear effective yield strength response of magnetorheological fluids, Preprint no. 2673, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2673 .
Abstract, PDF (1608 kByte)
We use the novel constitutive model in [15], derived using the homogenization method, to investigate the effect particle chain microstructures have on the properties of the magnetorheological fluid. The model allows to compute the constitutive coefficients for different geometries. Different geometrical realizations of chains can significantly change the magnetorheological effect of the suspension. Numerical simulations suggest that particle size is also important as the increase of the overall particle surface area can lead to a decrease of the overall magnetorheological effect while keeping the volume fraction constant. 
A. Mielke, A. Montefusco, M.A. Peletier, Exploring families of energydissipation landscapes via tilting  Three types of EDP convergence, Preprint no. 2668, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2668 .
Abstract, PDF (372 kByte)
This paper revolves around a subtle distinction between two concepts: passing to the limit in a family of gradient systems, on one hand, and deriving effective kinetic relations on the other. The two concepts are strongly related, and in many examples they even appear to be the same. Our main contributions are to show that they are different, to show that wellknown techniques developed for the former may give incorrect results for the latter, and to introduce new tools to remedy this. The approach is based on the EnergyDissipation Principle that provides a variational formulation to gradientflow equations that allows one to apply techniques from Γconvergence of functional on states and functionals on trajectories. 
A.F.M. TER Elst, A. Linke, J. Rehberg, On the numerical range of sectorial forms, Preprint no. 2667, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2667 .
Abstract, PDF (245 kByte)
We provide a sharp and optimal generic bound for the angle of the sectorial form associated to a nonsymmetric secondorder elliptic differential operator with various boundary conditions. Consequently this gives an, in general, sharper H^{∞}angle for the H^{∞}calculus on L_{p} for all p ∈ (1, ∞) if the coefficients are real valued. 
M. Kantner, Th. Höhne, Th. Koprucki, S. Burger, H.J. Wünsche, F. Schmidt, A. Mielke, U. Bandelow, Multidimensional modeling and simulation of semiconductor nanophotonic devices, Preprint no. 2653, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2653 .
Abstract, PDF (9836 kByte)
Selfconsistent modeling and multidimensional simulation of semiconductor nanophotonic devices is an important tool in the development of future integrated light sources and quantum devices. Simulations can guide important technological decisions by revealing performance bottlenecks in new device concepts, contribute to their understanding and help to theoretically explore their optimization potential. The efficient implementation of multidimensional numerical simulations for computeraided design tasks requires sophisticated numerical methods and modeling techniques. We review recent advances in devicescale modeling of quantum dot based singlephoton sources and laser diodes by selfconsistently coupling the optical Maxwell equations with semiclassical carrier transport models using semiclassical and fully quantum mechanical descriptions of the optically active region, respectively. For the simulation of realistic devices with complex, multidimensional geometries, we have developed a novel hpadaptive finite element approach for the optical Maxwell equations, using mixed meshes adapted to the multiscale properties of the photonic structures. For electrically driven devices, we introduced novel discretization and parameterembedding techniques to solve the driftdiffusion system for strongly degenerate semiconductors at cryogenic temperature. Our methodical advances are demonstrated on various applications, including verticalcavity surfaceemitting lasers, grating couplers and singlephoton sources. 
A. Mielke, A. Stephan, Coarsegraining via EDPconvergence for linear fastslow reaction systems, Preprint no. 2643, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2643 .
Abstract, PDF (426 kByte)
We consider linear reaction systems with slow and fast reactions, which can be interpreted as master equations or Kolmogorov forward equations for Markov processes on a finite state space. We investigate their limit behavior if the fast reaction rates tend to infinity, which leads to a coarsegrained model where the fast reactions create microscopically equilibrated clusters, while the exchange mass between the clusters occurs on the slow time scale. Assuming detailed balance the reaction system can be written as a gradient flow with respect to the relative entropy. Focusing on the physically relevant coshtype gradient structure we show how an effective limit gradient structure can be rigorously derived and that the coarsegrained equation again has a coshtype gradient structure. We obtain the strongest version of convergence in the sense of the EnergyDissipation Principle (EDP), namely EDPconvergence with tilting. 
A. Glitzky, M. Liero, G. Nika, Analysis of a hybrid model for the electrothermal behavior of semiconductor heterostructures, Preprint no. 2636, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2636 .
Abstract, PDF (355 kByte)
We prove existence of a weak solution for a hybrid model for the electrothermal behavior of semiconductor heterostructures. This hybrid model combines an electrothermal model based on driftdiffusion with thermistor type models in different subregions of the semiconductor heterostructure. The proof uses a regularization method and Schauder's fixed point theorem. For boundary data compatible with thermodynamic equilibrium we verify, additionally, uniqueness. Moreover, we derive bounds and higher integrability properties for the electrostatic potential and the quasi Fermi potentials as well as the temperature. 
A. Stephan, Combinatorial considerations on the invariant measure of a stochastic matrix, Preprint no. 2627, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2627 .
Abstract, PDF (225 kByte)
The invariant measure is a fundamental object in the theory of Markov processes. In finite dimensions a Markov process is defined by transition rates of the corresponding stochastic matrix. The Markov tree theorem provides an explicit representation of the invariant measure of a stochastic matrix. In this note, we given a simple and purely combinatorial proof of the Markov tree theorem. In the symmetric case of detailed balance, the statement and the proof simplifies even more. 
M.H. Farshbaf Shaker, M. Gugat, H. Heitsch, R. Henrion, Optimal Neumann boundary control of a vibrating string with uncertain initial data and probabilistic terminal constraints, Preprint no. 2626, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2626 .
Abstract, PDF (424 kByte)
In optimal control problems, often initial data are required that are not known exactly in practice. In order to take into account this uncertainty, we consider optimal control problems for a system with an uncertain initial state. A finite terminal time is given. On account of the uncertainty of the initial state, it is not possible to prescribe an exact terminal state. Instead, we are looking for controls that steer the system into a given neighborhood of the desired terminal state with sufficiently high probability. This neighborhood is described in terms of an inequality for the terminal energy. The probabilistic constraint in the considered optimal control problem leads to optimal controls that are robust against the inevitable uncertainties of the initial state. We show the existence of such optimal controls. Numerical examples with optimal Neumann control of the wave equation are presented. 
P. Colli, G. Gilardi, J. Sprekels, Asymptotic analysis of a tumor growth model with fractional operators, Preprint no. 2625, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2625 .
Abstract, PDF (341 kByte)
In this paper, we study a system of three evolutionary operator equations involving fractional powers of selfadjoint, monotone, unbounded, linear operators having compact resolvents. This system constitutes a generalized and relaxed version of a phase field system of CahnHilliard type modelling tumor growth that has originally been proposed in HawkinsDaarud et al. (Int. J. Numer. Math. Biomed. Eng. 28 (2012), 324). The original phase field system and certain relaxed versions thereof have been studied in recent papers coauthored by the present authors and E. Rocca. The model consists of a CahnHilliard equation for the tumor cell fraction φ, coupled to a reactiondiffusion equation for a function S representing the nutrientrich extracellular water volume fraction. Effects due to fluid motion are neglected. Motivated by the possibility that the diffusional regimes governing the evolution of the different constituents of the model may be of different (e.g., fractional) type, the present authors studied in a recent note a generalization of the systems investigated in the abovementioned works. Under rather general assumptions, wellposedness and regularity results have been shown. In particular, by writing the equation governing the evolution of the chemical potential in the form of a general variational inequality, also singular or nonsmooth contributions of logarithmic or of double obstacle type to the energy density could be admitted. In this note, we perform an asymptotic analysis of the governing system as two (small) relaxation parameters approach zero separately and simultaneously. Corresponding wellposedness and regularity results are established for the respective cases; in particular, we give a detailed discussion which assumptions on the admissible nonlinearities have to be postulated in each of the occurring cases. 
K.M. Gambaryan, T. Boeck, A. Trampert, O. Marquardt, Nucleation chronology and electronic properties of In(As,Sb,P) graded composition quantum dots grown on InAs(100) substrate, Preprint no. 2623, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2623 .
Abstract, PDF (745 kByte)
We provide a detailed study of nucleation process, characterization, electronic and optical properties of graded composition quantum dots (GCQDs) grown from InAsSbP composition liquid phase on an InAs(100) substrate in the StranskiKrastanov growth mode. Our GCQDs exhibit diameters from 10 to 120 nm and heights from 2 to 20 nm with segregation profiles having a maximum Sb content of approximately 20% at the top and a maximum P content of approximately 15% at the bottom of the GCQDs so that hole confinement is expected in the upper parts of the GCQDs. Using an eightband k · p model taking strain and builtin electrostatic potentials into account, we have computed the hole ground state energies and charge densities for a wide range of InAs_{1xy}Sb_{x}P_{y} GCQDs as close as possible to the systems observed in experiment. Finally, we have obtained an absorption spectrum for an ensemble of GCQDs by combining data from both experiment and theory. Excellent agreement between measured and simulated absorption spectra indicates that such GCQDs can be grown following a theoryguided design for application in specific devices. 
P. Colli, A. Signori, J. Sprekels, Optimal control of a phase field system modelling tumor growth with chemotaxis and singular potentials, Preprint no. 2614, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2614 .
Abstract, PDF (326 kByte)
A distributed optimal control problem for an extended model of phase field type for tumor growth is addressed. In this model, the chemotaxis effects are also taken into account. The control is realized by two control variables that design the dispensation of some drugs to the patient. The cost functional is of tracking type, whereas the potential setting has been kept quite general in order to allow regular and singular potentials to be considered. In this direction, some relaxation terms have been introduced in the system. We show the wellposedness of the state system, the Fréchet differentiability of the controltostate operator in a suitable functional analytic framework, and, lastly, we characterize the firstorder necessary conditions of optimality in terms of a variational inequality involving the adjoint variables. 
G. Alì, N. Rotundo, Existence and uniqueness of solution for multidimensional parabolic PDAEs arising in semiconductor modeling, Preprint no. 2607, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2607 .
Abstract, PDF (315 kByte)
This paper concerns with a compact network model combined with distributed models for semiconductor devices. For linear RLC networks containing distributed semiconductor devices, we construct a mathematical model that joins the differentialalgebraic initial value problem for the electric circuit with multidimensional parabolicelliptic boundary value problems for the devices. We prove an existence and uniqueness result, and the asymptotic behavior of this mixed initial boundary value problem of partial differentialalgebraic equations. 
TH. Frenzel, M. Liero, Effective diffusion in thin structures via generalized gradient systems and EDPconvergence, Preprint no. 2601, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2601 .
Abstract, PDF (359 kByte)
The notion of EnergyDissipationPrinciple convergence (EDPconvergence) is used to derive effective evolution equations for gradient systems describing diffusion in a structure consisting of several thin layers in the limit of vanishing layer thickness. The thicknesses of the sublayers tend to zero with different rates and the diffusion coefficients scale suitably. The FokkerPlanck equation can be formulated as gradientflow equation with respect to the logarithmic relative entropy of the system and a quadratic Wassersteintype gradient structure. The EDPconvergence of the gradient system is shown by proving suitable asymptotic lower limits of the entropy and the total dissipation functional. The crucial point is that the limiting evolution is again described by a gradient system, however, now the dissipation potential is not longer quadratic but is given in terms of the hyperbolic cosine. The latter describes jump processes across the thin layers and is related to the Marcelinde Donder kinetics. 
G. Nika, B. Vernescu, Multiscale modeling of magnetorheological suspensions, Preprint no. 2598, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2598 .
Abstract, PDF (3159 kByte)
We develop a multiscale approach to describe the behavior of a suspension of solid magnetizable particles in a viscous nonconducting fluid in the presence of an externally applied magnetic field. By upscaling the quasistatic Maxwell equations coupled with the Stokes' equations we are able to capture the magnetorheological effect. The model we obtain generalizes the one introduced by Neuringer & Rosensweig for quasistatic phenomena. We derive the macroscopic constitutive properties explicitly in terms of the solutions of local problems. The effective coefficients have a nonlinear dependence on the volume fraction when chain structures are present. The velocity profiles computed for some simple flows, exhibit an apparent yield stress and the flowprofile resembles a Bingham fluid flow. 
B. Franchi, M. Heida, S. Lorenzani, A mathematical model for Alzheimer's disease: An approach via stochastic homogenization of the Smoluchowski equation, Preprint no. 2595, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2595 .
Abstract, PDF (452 kByte)
In this note, we apply the theory of stochastic homogenization to find the asymptotic behavior of the solution of a set of Smoluchowski's coagulationdiffusion equations with nonhomogeneous Neumann boundary conditions. This system is meant to model the aggregation and diffusion of βamyloid peptide (Aβ) in the cerebral tissue, a process associated with the development of Alzheimer's disease. In contrast to the approach used in our previous works, in the present paper we account for the nonperiodicity of the cellular structure of the brain by assuming a stochastic model for the spatial distribution of neurons. Further, we consider nonperiodic random diffusion coefficients for the amyloid aggregates and a random production of Aβ in the monomeric form at the level of neuronal membranes. 
M. Heida, S. Neukamm, M. Varga, Stochastic homogenization of Lambdaconvex gradient flows, Preprint no. 2594, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2594 .
Abstract, PDF (429 kByte)
In this paper we present a stochastic homogenization result for a class of Hilbert space evolutionary gradient systems driven by a quadratic dissipation potential and a Λconvex energy functional featuring random and rapidly oscillating coefficients. Specific examples included in the result are AllenCahn type equations and evolutionary equations driven by the pLaplace operator with p ∈ in (1, ∞). The homogenization procedure we apply is based on a stochastic twoscale convergence approach. In particular, we define a stochastic unfolding operator which can be considered as a random counterpart of the wellestablished notion of periodic unfolding. The stochastic unfolding procedure grants a very convenient method for homogenization problems defined in terms of (Λ)convex functionals. 
A. Glitzky, M. Liero, G. Nika, An existence result for a class of electrothermal driftdiffusion models with GaussFermi statistics for organic semiconductors, Preprint no. 2593, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2593 .
Abstract, PDF (387 kByte)
This work is concerned with the analysis of a driftdiffusion model for the electrothermal behavior of organic semiconductor devices. A "generalized Van Roosbroeck” system coupled to the heat equation is employed, where the former consists of continuity equations for electrons and holes and a Poisson equation for the electrostatic potential, and the latter features source terms containing Joule heat contributions and recombination heat. Special features of organic semiconductors like GaussFermi statistics and mobilities functions depending on the electric field strength are taken into account. We prove the existence of solutions for the stationary problem by an iteration scheme and Schauder's fixed point theorem. The underlying solution concept is related to weak solutions of the Van Roosbroeck system and entropy solutions of the heat equation. Additionally, for data compatible with thermodynamic equilibrium, the uniqueness of the solution is verified. It was recently shown that selfheating significantly influences the electronic properties of organic semiconductor devices. Therefore, modeling the coupled electric and thermal responses of organic semiconductors is essential for predicting the effects of temperature on the overall behavior of the device. This work puts the electrothermal driftdiffusion model for organic semiconductors on a sound analytical basis. 
A.F.M. TER Elst, R. HallerDintelmann, J. Rehberg, P. Tolksdorf, On the $L^p$theory for secondorder elliptic operators in divergence form with complex coefficients, Preprint no. 2590, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2590 .
Abstract, PDF (383 kByte)
Given a complex, elliptic coefficient function we investigate for which values of p the corresponding secondorder divergence form operator, complemented with Dirichlet, Neumann or mixed boundary conditions, generates a strongly continuous semigroup on L^{p}(Ω). Additional properties like analyticity of the semigroup, H^{∞}calculus and maximal regularity arealso discussed. Finally we prove a perturbation result for real coefficients that gives the whole range of ^{p}'s for small imaginary parts of the coefficients. Our results are based on the recent notion of ^{p}ellipticity, reverse Hölder inequalities and Gaussian estimates for the real coefficients. 
P. Colli, G. Gilardi, J. Sprekels, Longtime behavior for a generalized CahnHilliard system with fractional operators, Preprint no. 2588, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2588 .
Abstract, PDF (248 kByte)
In this contribution, we deal with the longtime behavior of the solutions to the fractional variant of the CahnHilliard system, with possibly singular potentials, which we recently investigated in the paper "Wellposedness and regularity for a generalized fractional CahnHilliard system". More precisely, we give a complete characterization of the Omegalimit of the phase parameter. The characterization depends on the first eigenvalue of one of the involved operators: if this eigenvalue is positive, then the chemical potential vanishes at infinity, and every element of the Omegalimit is a stationary solution to the phase equation; if it is zero instead, then every element of the Omegalimit solves a problem containing a real function which is related to the chemical potential. Such a function is nonunique and time dependent, in general, as we show by means of an example; however, we give sufficient conditions for it to be uniquely determined and constant. 
A. Mielke, T. Roubíček, Thermoviscoelasticity in KelvinVoigt rheology at large strains, Preprint no. 2584, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2584 .
Abstract, PDF (472 kByte)
The frameindifferent thermodynamicallyconsistent model of thermoviscoelasticity at large strain is formulated in the reference configuration with using the concept of the secondgrade nonsimple materials. We focus on physically correct viscous stresses that are frame indifferent under timedependent rotations. Also elastic stresses are frame indifferent under rotations and respect positivity of the determinant of the deformation gradient. The heat transfer is governed by the Fourier law in the actual deformed configuration, which leads to a nontrivial description when pulled back into the reference configuration. Existence of weak solutions in the quasistatic setting, i.e. inertial forces are ignored, is shown by time discretization. 
R. Rossi, U. Stefanelli, M. Thomas, Rateindependent evolution of sets, Preprint no. 2578, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2578 .
Abstract, PDF (475 kByte)
The goal of this work is to analyze a model for the rateindependent evolution of sets with finite perimeter. The evolution of the admissible sets is driven by that of a given timedependent set, which has to include the admissible sets and hence is to be understood as an external loading. The process is driven by the competition between perimeter minimization and minimization of volume changes. In the mathematical modeling of this process, we distinguish the adhesive case, in which the constraint that the (complement of) the `external load' contains the evolving sets is penalized by a term contributing to the driving energy functional, from the brittle case, enforcing this constraint. The existence of Energetic solutions for the adhesive system is proved by passing to the limit in the associated timeincremental minimization scheme. In the brittle case, this timediscretization procedure gives rise to evolving sets satisfying the stability condition, but it remains an open problem to additionally deduce energydissipation balance in the timecontinuous limit. This can be obtained under some suitable quantification of data. The properties of the brittle evolution law are illustrated by numerical examples in two space dimensions. 
A.F.M. TER Elst, H. Meinlschmidt, J. Rehberg, Essential boundedness for solutions of the Neumann problem on general domains, Preprint no. 2574, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2574 .
Abstract, PDF (220 kByte)
Let the domain under consideration be bounded. Under the suppositions of very weak Sobolev embeddings we prove that the solutions of the Neumann problem for an elliptic, second order divergence operator are essentially bounded, if the right hand sides are taken from the dual of a Sobolev space which is adapted to the above embedding.
Talks, Poster

O. Marquardt, Datadriven electronic structure calculations for semiconductor nanostructures, Efficient algorithms for numerical problems  Workshop on the occasion of the retirement of Peter Mathé, January 17, 2020, WIAS Berlin, January 17, 2020.

G. Nika, An existence result for a class of electrothermal driftdiffusion models with FermiGauss statistics for organic semiconductors, Joint Mathematics Meeting, January 15  18, 2020, American Mathematical Society/ Mathematical Association of America, Denver, USA, January 15, 2020.

D. Peschka, Mathematical modeling and simulation of flows and the interaction with a substrate using energetic variational methods, Vortrag im Rahmen des SFB1194, Technische Universität Darmstadt, January 22, 2020.

D. Peschka , Variational modeling of bulk and interface effects in fluid dynamics, SPP 2171 Advanced School ``Introduction to Wetting Dynamics'', February 17  21, 2020, Westfälische WilhelmsUniversität Münster, February 18, 2020.

A. Stephan, Coarsegraining via EDPconvergence for linear fastslow reaction systems, Seminar ``Applied Analysis'', Eindhoven University of Technology, Centre for Analysis, Scientific Computing, and Applications  Mathematics and Computer Science, Netherlands, January 20, 2020.

A. Stephan, On mathematical coarsegraining for linear reaction systems, 8th BMS Student Conference, February 19  21, 2020, Technische Universität Berlin, February 21, 2020.

M. Thomas, Nonlinear fraction dynamics: modeling, analysis, approximation, and applications, Vorstellung der Projektanträge im SPP 2256, Bad Honnef, January 30, 2020.

J. Fuhrmann, D.H. Doan, A. Glitzky, M. Liero, G. Nika, Unipolar driftdiffusion simulation of Sshaped currentvoltage relations for organic semiconductor devices, Finite Volumes for Complex Applications IX (Online Event), Bergen, Norway, June 15  19, 2020.

TH. Koprucki, Nonisothermal ScharfetterGummel scheme for electrothermal transport simulation in degenerate semiconductors, Finite Volumes for Complex Applications IX (Online Event), June 15  19, 2020, University of Bergen, Bergen, Norway, June 16, 2020, DOI 10.1007/9783030436513_14 .

M. Liero, A. Mielke, Analysis for thermomechanical models with internal variables, Vorstellung der Projektanträge im SPP 2256, Bad Honnef, January 30, 2020.

A. Mielke, Finitestrain viscoelasticity with temperature coupling, Calculus of Variations and Applications, January 27  February 1, 2020, Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste, Italy, January 28, 2020.

A. Mielke, Gradient systems and evolutionary Gammaconvergence (online talk), Oberseminar ``Mathematik in den Naturwissenschaften'', JuliusMaximiliansUniversität Würzburg, June 5, 2020.

J. Rehberg, Explicit and uniform estimates for second order divergence operators on L^{p} spaces, Oberseminar ``Analysis und Theoretische Physik'', Leibniz Universität Hannover, Institut für Angewandte Mathematik, January 28, 2020.

A. Maltsi, Th. Koprucki, T. Streckenbach, K. Tabelow, J. Polzehl, Modelbased geometry reconstruction of quantum dots from TEM, Microscopy Conference 2019, Poster session IM 4, Berlin, September 1  5, 2019.

A. Maltsi, Th. Koprucki, T. Streckenbach, K. Tabelow, J. Polzehl, Modelbased geometry reconstruction of quantum dots from TEM, BMS Summer School 2019: Mathematics of Deep Learning, Berlin, August 19  30, 2019.

A. Maltsi, Modelbased geometry reconstruction in TEM images, Sondierungsworkshop MPIE/WIAS ``Elektrochemie, Halbleiternanostrukturen und Metalle", October 14  15, 2019, MaxPlanckInstitut für Eisenforschung GmbH Düsseldorf, October 15, 2019.

A. Maltsi, Modelbased geometry reconstruction in TEM images, Sondierungsworkshop MPIE/WIAS ``Elektrochemie, Halbleiternanostrukturen und Metalle", October 14  November 15, 2019, MaxPlanckInstitut für Eisenforschung GmbH Düsseldorf, October 15, 2019.

A. Maltsi, Towards modelbased geometry reconstruction of quantum dots from TEM, ``9th International Congress on Industrial and Applied Mathematics" (ICIAM 2019), July 15  19, 2019, Universitat de València, Spain, July 19, 2019.

M.H. Farshbaf Shaker, D. Peschka, M. Thomas, Modeling and analysis of suspension flows, Visit of the Scientific Advisory Board of MATH+, November 11, 2019.

M.H. Farshbaf Shaker, D. Peschka, M. Thomas, Modeling and analysis of suspension flows, 1st MATH+ Day, Berlin, December 13, 2019.

M. Heida, A. Mielke, A. Stephan, Effective models for materials and interfaces with multiple scales, SCCS Days 2019 of the Collaborative Research Center  CRC 1114, Zeuthen, May 20  22, 2019.

M. Heida, Convergences of the squareroot approximation scheme to the FokkerPlanck operator, ``9th International Congress on Industrial and Applied Mathematics" (ICIAM 2019), July 15  19, 2019, Universitat de València, Spain, July 17, 2019.

M. Heida, Stochastic homogenization of PDE on nonuniformly Lipschitz and percolating structures, DMVJahrestagung 2019, September 23  26, 2019, KIT  Karlsruher Institut für Technologie, September 24, 2019.

M. Heida, The SQRA operator: Convergence behaviour and applications, Universität Wien, Fakultät für Mathematik, Lehrstuhl Analysis, Austria, March 19, 2019.

M. Heida, The fractional pLaplacian emerging from discrete homogenization of the random conductance model with degenerate ergodic weights, 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2019), Section S14 ``Applied Analysis'', February 18  22, 2019, Universität Wien, Technische Universität Wien, Austria, February 19, 2019.

M. Heida, What is... SQRA discretization of the FokkerPlanck equation?, CRC1114 Colloquium, Freie Universität Berlin, SFB 1114, April 25, 2019.

O. Marquardt, Charge confining mechanisms in IIIV semiconductor nanowires, 19th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2019), July 8  12, 2019, University of Ottawa, Canada, July 8, 2019.

O. Marquardt, Datadriven electronic structure calculations for nanostructures (DESCANT), Sondierungsworkshop MPIE/WIAS ``Elektrochemie, Halbleiternanostrukturen und Metalle", October 14  15, 2019, MaxPlanckInstitut für Eisenforschung GmbH Düsseldorf, October 15, 2019.

O. Marquardt, Modelling the electronic properties of semiconductor nanowires, Engineering Physics Seminar, McMaster University, Hamilton, Canada, July 12, 2019.

G. Nika, An existence result for a class of electrothermal driftdiffusion models with GaussFermi statistics for organic semiconductors, DMVJahrestagung 2019, September 23  26, 2019, KIT  Karlsruher Institut für Technologie.

G. Nika, Homogenization for a multiscale model of magnetorheological suspension, 9th International Congress on Industrial and Applied Mathematics (ICIAM 2019), Minisymposium MS ME13 1 ``Emerging Problems in the Homogenization of Partial Differential Equations'', July 15  19, 2019, Valencia, Spain, July 15, 2019.

D. Peschka, Dynamic contact angles via generalized gradient flows, Modelling of Thin Liquid Films  Asymptotic Approach vs. Gradient Dynamics, April 28  May 3, 2019, Banff International Research Station for Mathematical Information and Discovery, Canada, April 30, 2019.

D. Peschka, Dynamic contact angles via gradient flows, 694. WEHeraeusSeminar ``Wetting on Soft or Microstructured Surfaces'', Bad Honnef, April 10  13, 2019.

D. Peschka, Gradient formulations with flow maps  Mathematical and numerical approaches to free boundary problems, Kolloquium des Graduiertenkollegs 2339 ``Interfaces, Complex Structures, and Singular Limits'', Universität Regensburg, May 24, 2019.

D. Peschka, Gradient structures for flows of concentrated suspensions  jamming and free boundaries, 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2019), Section S11 ``Interfacial Flows", February 18  22, 2019, Technische Universität Wien, Austria, February 20, 2019.

D. Peschka, Mathematical modeling and simulation of substrateflow interaction using generalized gradient flow, Begutachtungskolloquium für die Anträge des SPP 2171 ``Dynamische Benetzung flexibler, adaptiver und schaltbarer Oberflächen'', Mainz, February 7  8, 2019.

D. Peschka, Mathematical modeling of fluid flows using gradient systems, Seminar in PDE and Applications, Delft University of Technology, Netherlands, May 28, 2019.

D. Peschka, Steering pattern formation of viscous flows, DMVJahrestagung 2019, Sektion ``Differentialgleichungen und Anwendungen'', September 23  26, 2019, KIT  Karlsruher Institut für Technologie, September 23, 2019.

D. Peschka, ``Numerical methods for charge transport in semiconductors: FEM vs FV", 9th International Congress on Industrial and Applied Mathematics (ICIAM 2019), July 15  19, 2019, Valencia, Spain, July 17, 2019.

A. Stephan, EDPconvergence for linear reaction diffusion systems with different time scales, Calculus of Variations on Schiermonnikoog 2019, July 1  5, 2019, Utrecht University, Schiermonnikoog, Netherlands, July 2, 2019.

A. Stephan, EDPconvergence for linear reactiondiffusion systems with different time scales, Winter School ``Gradient Flows and Variational Methods in PDEs'', November 25  29, 2019, Universität Ulm, November 29, 2019.

A. Stephan, Evolutionary Gammaconvergence for a linear reactiondiffusion system with different time scales, COPDESCWorkshop ``Calculus of Variation and Nonlinear Partial Differential Equations", March 25  28, 2019, Universität Regensburg, March 26, 2019.

A. Stephan, Evolutionary Gammaconvergence for a linear reactiondiffusion system with different time scales, 9th International Congress on Industrial and Applied Mathematics (ICIAM 2019), July 15  19, 2019, Universitat de València, Spain, July 16, 2019.

A. Stephan, On evolution semigroups and Trotter product operatornorm estimates, Operator Theory and Krein Spaces, December 19  22, 2019, Technische Universität Wien, Austria, December 20, 2019.

A. Stephan, Rigorous derivation of the effective equation of a linear reaction system with different time scales, 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2019), Section S14 ``Applied Analysis'', February 18  22, 2019, Universität Wien, Technische Universität Wien, Austria, February 21, 2019.

S. Tornquist, Variational problems involving Caccioppoli partitions, 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2019), Section S14 ``Applied Analysis", February 18  22, 2019, Technische Universität Wien, Austria, February 19, 2019.

A. Zafferi, An approach to multiphase flows in geosciences, MURPHYSHSFS 2019 Summer School on MultiRate Processes, SlowFast Systems and Hysteresis, Turin, Italy, June 17  21, 2019.

A. Zafferi, Dynamics of rock dehydration on multiple scales, SCCS Days 2019 of the Collaborative Research Center  CRC 1114, Zeuthen, May 20  22, 2019.

A. Zafferi, Some regularity results for a nonisothermal CahnHilliard model, 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2019), Section S14 ``Applied Analysis'', February 18  22, 2019, Technische Universität Wien, Austria, February 20, 2019.

J. Sprekels, Optimal control of a CahnHilliardDarcy system with mass source modeling tumor growth, Università degli Studi di Pavia, Dipartimento di Matematica, Italy, May 14, 2019.

A. Glitzky, An existence result for a class of electrothermal driftdiffusion models with GaussFermi statistics for organic semiconductors, ``Partial Differential Equations in Fluids and Solids" (PDE2019), September 9  13, 2019, WIAS Berlin, September 12, 2019.

A. Glitzky, Driftdiffusion problems with GaussFermi statistics and fielddependent mobility for organic semiconductor devices, 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2019), Section S14 ``Applied Analysis'', February 18  22, 2019, Universität Wien, Technische Universität Wien, Austria, February 22, 2019.

K. Hopf, On the singularity formation and relaxation to equilibrium in 1D FokkerPlanck model with superlinear drift, Winter School ``Gradient Flows and Variational Methods in PDEs'', November 25  29, 2019, Universität Ulm, November 25, 2019.

K. Hopf, On the singularity formation and relaxation to equilibrium in 1D FokkerPlanck model with superlinear drift, Gradient Flows and Variational Methods in PDEs, November 25  29, 2019, Universität Ulm, November 25, 2019.

M. Thomas, Analysis for the discrete approximation of gradientregularized damage models, Mathematics Seminar Brescia, Università degli Studi di Brescia, Italy, March 13, 2019.

M. Thomas, Analysis for the discrete approximation of gradientregularized damage models, PDE Afternoon, Universität Wien, Austria, April 10, 2019.

M. Thomas, Analytical and numerical aspects for the approximation of gradientregularized damage models, 9th International Congress on Industrial and Applied Mathematics (ICIAM 2019), Thematic Minisymposium MS A3226 ``PhaseField Models in Simulation and Optimization'', July 15  19, 2019, Valencia, Spain, July 17, 2019.

M. Thomas, Analytical and numerical aspects of rateindependent gradientregularized damage models, Conference ``Dynamics, Equations and Applications (DEA 2019)'', Session D444 ``Topics in the Mathematical Modelling of Solids'', September 16  20, 2019, AGH University of Science and Technology, Kraków, Poland, September 19, 2019.

M. Thomas, Coupling of rateindependent and ratedependent systems, MURPHYSHSFS 2019 Summer School on MultiRate Processes, SlowFast Systems and Hysteresis, June 17  19, 2019, Politecnico di Torino, Turin, Italy.

M. Thomas, Coupling of rateindependent and ratedependent systems with application to delamination processes in solids, Mathematics for Mechanics, October 29  November 1, 2019, Czech Academy of Sciences, Prague, Czech Republic, October 31, 2019.

M. Thomas, Coupling of rateindependent and ratedependent systems with application to delamination processes in solids, Seminar ``Applied and Computational Analysis'', University of Cambridge, UK, October 10, 2019.

M. Thomas, Dynamics of rock dehydration on multiple scales, SCCS Days 2019 of the Collaborative Research Center  CRC 1114, May 20  22, 2019, Freie Universität Berlin, Zeuthen, May 21, 2019.

M. Thomas, GENERIC structures with bulkinterface interaction, SFB 910 Symposium ``Energy Based Modeling, Simulation and Control'', October 25, 2019, Technische Universität Berlin, October 25, 2019.

M. Thomas, Gradient structures for flows of concentrated suspensions, 9th International Congress on Industrial and Applied Mathematics (ICIAM 2019), Thematic Minisymposium MS ME775 ``Recent Advances in Understanding Suspensions and Granular Media Flow'', July 15  19, 2019, Valencia, Spain, July 17, 2019.

M. Thomas, Rateindependent evolution of sets and application to fracture processes, 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2019), Section S14 ``Applied Analysis'', February 18  22, 2019, Technische Universität Wien, Austria, February 20, 2019.

M. Heida, The SQRA operator: Convergence behaviour and applications, Politechnico di Milano, Dipartimento di Matematica, Italy, March 13, 2019.

TH. Koprucki, Datenmanagement  Forschungsdaten in Modellierung und Simulation, BlockSeminar des SFB 787 ``Nanophotonik'', May 6  8, 2019, Technische Universität Berlin, GraalMüritz, May 6, 2019.

TH. Koprucki, Math4NFDI  a consortium for mathematics, Getting Ready: Leibniz in der Nationalen Forschungsdateninfrastruktur (NFDI), June 5, 2019, Leibniz Geschäftsstelle, Berlin, June 5, 2019.

TH. Koprucki, Model pathway diagrams for the representation of mathematical models, DMVJahrestagung 2019, Minisymposium ``FAIRmath: Opening mathematical research data for the next generation", September 23  26, 2019, KIT  Karlsruher Institut für Technologie, September 24, 2019.

TH. Koprucki, Multidimensional modeling and simulation of semiconductor devices, Physikalisches Kolloquium, Technische Universität Chemnitz, Institut für Physik, November 27, 2019.

TH. Koprucki, On a database of simulated TEM images for In(Ga)As/GaAs quantum dots with various shapes, 19th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2019) , Session ``Nanostructures", July 8  12, 2019, University of Ottawa, Canada, July 8, 2019.

TH. Koprucki, Towards multiscale modeling of IIINbased LEDs, 19th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2019) , Session ``Postdeadline Session and Outlook", July 8  12, 2019, University of Ottawa, Canada, July 12, 2019.

M. Liero, Effective diffusion in thin structures via generalized gradient systems and EDPconvergence, 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2019), Section S14 ``Applied Analysis'', February 18  22, 2019, Universität Wien, Technische Universität Wien, Austria, February 20, 2019.

A. Mielke, An existence result for thermoviscoelasticity at finite strains, Mathematics for Mechanics, October 29  November 1, 2019, Czech Academy of Sciences, Institute for Information Theory and Automation, Prague, Czech Republic, November 1, 2019.

A. Mielke, Effective kinetic relations and EDP convergence, COPDESCWorkshop ``Calculus of Variation and Nonlinear Partial Differential Equations'', March 25  28, 2019, Universität Regensburg, March 28, 2019.

A. Mielke, Effective kinetic relations and EDP convergence for gradient systems, Necas Seminar on Continuum Mechanics, Charles University, Prague, Czech Republic, March 18, 2019.

A. Mielke, Evolutionary Gammaconvergence for gradient systems, Mathematisches Kolloquium, AlbertLudwigsUniversität Freiburg, January 24, 2019.

A. Mielke, Gamma convergence of dissipation functionals and EDP convergence for gradient systems, 6th Applied Mathematics Symposium Münster: Recent Advances in the Calculus of Variations, September 16  19, 2019, Westfälische WilhelmsUniversität Münster, September 17, 2019.

A. Mielke, Gradient systems and evolutionary Gammaconvergence, DMVJahrestagung 2019, September 23  26, 2019, KIT  Karlsruher Institut für Technologie, September 24, 2019.

A. Mielke, On Kolmogorov's twoequation model for turbulence, 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2019), Section S14 ``Applied Analysis'', February 18  22, 2019, Universität Wien, Technische Universität Wien, Austria, February 21, 2019.

A. Mielke, On initialboundary value problems for materials with internal variables or temperature dependence, Workshop on Mathematical Methods in Continuum Physics and Engineering: Theory, Models, Simulation, November 6  7, 2019, Technische Universität Darmstadt, November 6, 2019.

A. Mielke, Pattern formation in coupled parabolic systems on extended domains, Fundamentals and Methods of Design and Control of Complex Systems  Introductory Lectures 2019/20 of CRC 910, Technische Universität Berlin, November 25, 2019.

A. Mielke, Thermodynamical modeling via GENERIC: From quantum mechanics to semiconductor devices, Institute of Thermomechanics's Seminar, Czech Academy of Sciences, Prague, March 21, 2019.

A. Mielke, Variational methods in timedependent material models with finitestrain deformations, Hausdorff School on Modeling and Analysis of Evolutionary Problems in Materials Science, September 23  27, 2019, Hausdorff Center for Mathematics, Universität Bonn.

A. Mielke, EDP convergence for the membrane limit in the porous medium equation, 9th International Congress on Industrial and Applied Mathematics (ICIAM 2019), Thematic Minisymposium MS ME13 9 ``Entropy Methods for Multidimensional Systems in Mechanics'', July 15  19, 2019, Valencia, Spain, July 19, 2019.

A. Mielke, Effective models for materials and interfaces with multiple scales, SCCS Days 2019 of the Collaborative Research Center  CRC 1114, May 20  22, 2019, SFB 1114, Freie Universität Berlin, Zeuthen, May 21, 2019.

A. Mielke, Gradient systems and the derivation of effective kinetic relations via EDP convergence, Material Theories, Statistical Mechanics, and Geometric Analysis: A Conference in Honor of Stephan Luckhaus' 66th Birthday, June 3  6, 2019, MaxPlanckInstitut für Mathematik in den Naturwissenschaften, Leipzig, June 5, 2019.

A. Mielke, Transport versus growth and decay: The (spherical) HellingerKantorovich distance between arbitrary measures, Optimal Transport: From Geometry to Numerics, May 13  17, 2019, Erwin Schrödinger International Institute for Mathematics and Physics, Universität Wien, Austria, May 17, 2019.

J. Rehberg, An extrapolation for the LaxMilgram isomorphism for second order divergence operators, Oberseminar ``Angewandte Analysis'', Technische Universität Darmstadt, February 7, 2019.

J. Rehberg, Explicit and uniform estimates for second order divergence operators on $L^P$ spaces, Evolution Equations: Applied and Abstract Perspectives, October 28  November 1, 2019, Centre International de Rencontres Mathématiques (CIRM), Luminy, France, October 31, 2019.

J. Rehberg, Maximal parabolic regularity for the treatment of real world problems, 12th Workshop on Analysis and Advanced Numerical Methods for Partial Differential Equations (not only) for Junior Scientists (AANMPDE 12), July 1  5, 2019, Österreichische Akademie der Wissenschaften, St. Wolfgang / Strobl, Austria, July 2, 2019.

J. Rehberg, Wellposedness for the KellerSegel model  based on a pioneering result of Herbert Amann, International Conference ``Nonlinear Analysis'' in Honor of Herbert Amann's 80th Birthday, June 11  14, 2019, Scuola Normale Superiore di Pisa, Cortona, Italy, June 11, 2019.

S. Tornquist, Towards the analysis of dynamic phasefield fracture, Spring School on Variational Analysis 2019, Paseky, Czech Republic, May 19  25, 2019.

S. Tornquist, Towards the analysis of dynamic phasefield fracture, MURPHYSHSFS 2019 Summer School on MultiRate Processes, SlowFast Systems and Hysteresis, Turin, Italy, June 17  21, 2019.
Research Groups
 Partial Differential Equations
 Laser Dynamics
 Numerical Mathematics and Scientific Computing
 Nonlinear Optimization and Inverse Problems
 Interacting Random Systems
 Stochastic Algorithms and Nonparametric Statistics
 Thermodynamic Modeling and Analysis of Phase Transitions
 Nonsmooth Variational Problems and Operator Equations