Preprints
- M. Heida, A. Sikorski und M. Weber Consistency and order 1 convergence of cell-centered finite volume discretizations of degenerate elliptic problems in any space dimension, 2022 ( Preprint )
- A. Stephan and H. Stephan Positivity and polynomial decay of energies for square-field operators, 2021 ( Preprint )
- A. Stephan Coarse-graining and reconstruction for Markov matrices, 2021 ( Preprint )
- J. Fischer, K. Hopf, M. Kniely, and A. Mielke Global existence analysis of energy-reaction-diffusion systems, 2021 ( Preprint )
- M. Heida Stochastic homogenization on randomly perforated domains, 2020 ( Preprint )
- A. Stephan Combinatorial considerations on invariant measures of stochastic matrices, 2019 ( Preprint )
Publications in refereed journals
- M. Heida, M. Kantner, and A. Stephan Consistency and convergence for a family of finite volume discretizations of the Fokker--Planck operator.
ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN), 2021 ( Preprint ) - A. Stephan EDP-convergence for a linear reaction-diffusion system with fast reversible reaction.
Calculus of Variations and Partial Differential Equations, 60, 2021 ( Preprint ) - A. Mielke, M. A. Peletier, and A. Stephan EDP-convergence for nonlinear fast-slow reaction systems with detailed balance.
Nonlinearity, 34:8, 2021 ( Preprint ) - A. Mielke, A. Montefusco, and M. A. Peletier Exploring families of energy-dissipation landscapes via tilting:
three types of EDP convergence.
Contin. Mech. Thermodyn., 33:611-637, 2021 ( Preprint ) - M. Heida, S. Neukamm, and M. Varga Stochastic homogenization of Λ-convex gradient flows.
Discrete and Continuous Dynamical Systems - S, 14:1, 611-637, 2021 ( Preprint ) - A. Mielke, R. Netz, and S. Zendehroud A rigorous derivation and energetics of a wave equation with fractional
damping.
J. Evolution Equations, 21:3079-3102, 2021 ( Preprint ) - J. Maas and A. Mielke Modeling of chemical reaction systems with detailed balance using gradient structures.
J. Stat. Physics, 181:2257-2303, 2020 ( Preprint ) - O. Souček , M. Heida, and J. Málek On a thermodynamic framework for developing boundary conditions for Korteweg fluids.
International Journal of Engineering Science, 154, 2020 ( Preprint ) - B. Franchi, M. Heida, and S. Lorenzani A mathematical model for Alzheimer´s disease: An approach via stochastic homogenization of the Smoluchowski equation.
Communications in Mathematical Sciences, 18(4):1105-1134, 2020 ( Preprint ) - M. Heida, R. Kornhuber, and J. Podlesny Fractal homogenization of multiscale interface problems.
SIAM Multiscale Modeling and Simulation, 18(1):294-314, 2020 ( Preprint ) - P. Gussmann, A. Mielke Linearized elasticity as Mosco-limit of finite elasticity in the presence of cracks. Advances in Calculus of Variations. 13(1):33-52, 2020 (Preprint)
- F. Flegel, M. Heida The fractional p-Laplacian emerging from homogenization of the random conductance model with degenerate ergodic weights and unbounded-range jumps.
Calculus of Variations and Partial Differential Equations, 59(1):8, 2020 ( Preprint ) - A. Mielke and A. Stephan Coarse graining via EDP-convergence for linear fast-slow reaction systems.
Math. Models Meth. Appl. Sci., 30(9):1765-1807, 2020 ( Preprint ) - P. Dondl, T. Frenzel, and A. Mielke A gradient system with a wiggly energy and relaxed EDP-convergence.
ESAIM Control Optim. Calc. Var., 25, 68:1-45, 2019 ( Preprint ) - H. Stephan and A. Stephan Memory equations as reduced Markov processes.
Discrete Contin. Dyn. Syst., 39:2133-2155, 2019. ( Preprint ) - F. Flegel, M. Heida, and M. Slowik Homogenization theory for the random conductance model with degenerate ergodic weights and unbounded-range jumps.
Annales de l’Institut Henri Poincaré probabilités et statistiques, 55(3):1226-1257, 2019 ( Preprint ) - M. Heida, S. Nesenenko Stochastic homogenization of rate-dependent models of monotone type in plasticity.
Asymptotic Analysis, 112(3-4):185-212, 2019 ( Preprint ) - MH, R. I. Patterson, and D. M. Renger Topologies and measures on the space of functions of bounded variation taking values in a Banach or metric space.
Journal of Evolution Equations, 19(1):111-152, 2019 ( Preprint ) - M. Heida, M. Röger Large deviation principle for a stochastic Allen--Cahn equation.
Journal of Theoretical Probability, 31(1):364-401, 2018 ( Preprint ) - M. Heida Convergences of the squareroot approximation scheme to the Fokker--Planck operator.
Mathematical Models and Methods in Applied Sciences, 28(13):2599-2635, 2018 ( Preprint ) - L. Donati, M. Heida, B. G. Keller, and M. Weber Estimation of the infinitesimal generator by square-root approximation.
Journal of Physics: Condensed Matter, 30(42):425201, 2018 ( Preprint ) - A. Mielke, M. Mittnenzweig: Convergence to equilibrium in energy-reaction-diffusion systems using vector-valued functional inequalities. J. Nonlin. Science, 28(2):765-806, 2018 ( Preprint )
- M. Liero, A. Mielke, G. Savaré. Optimal entropy-transport problems and a new Hellinger--Kantorovich distance. Inventiones mathematicae, 211(3):969-1117, 2018. ( Preprint )
- M. Heida Stochastic homogenization of rate-independent systems and applications.
Continuum Mechanics and Thermodynamics May 2017, Volume 29, Issue 3, pp 853-894 ( Preprint ) - M. Heida and A. Mielke Averaging of time-periodic dissipation potentials in rate-independent processes.
DCDS-S Discrete Contin. Dyn. Syst. 10 (6): 1303-1327, 2017 ( Preprint ) - M. Heida and Ben Schweizer Stochastic homogenization of plasticity equations.
ESAIM: Control, Optimisation and Calculus of Variations, 24(1):153-176, 2018. ( Preprint ) - M. Liero, A. Mielke, M. Peletier, D.R.M. Renger. On microscopic origins of generalized gradient structures. DCDS-S Discrete Contin. Dyn. Syst. 10 (1): 1-35, 2017 (Proceedings of STAMM 2014 in Poitiers).
- A. Mielke, R. Patterson, M. Peletier, M. Renger. Non-equilibrium thermodynamical principles for chemical reactions with mass-action kinetics. SIAM J. Appl. Math., 77(4): 1562-1585, 2017. ( Preprint )
- A. Mielke, D.R.M. Renger, M.A. Peletier: A generalization of Onsagers reciprocity relations to gradient flows with nonlinear mobility. J. Non-Equil. Thermodyn. 141-149, 41(2), 2016. ( Preprint )
- M. Liero, A. Mielke, G. Savaré: Optimal transport in competition with reaction -- the Hellinger-Kantorovich distance and geodesic curves. SIMA 2869-2911 48(4) 2016.
- A. Mielke, R. Rossi, G. Savaré. Global existence results for viscoplasticity at finite strain. Archive Rat. Mech. Analysis 227 (1). pp. 423-475.( Preprint )
- A. Mielke, R. Rossi, G. Savaré. Balanced-Viscosity solutions for multi-rate systems. J. Phys., MURPHYS-HSFS Proc., eds. O. Klein et al., vol. 727 (1), article 012010, 26 pages, 2016. ( Preprint )
- E. Bonetti, E. Rocca, R. Rossi and M. Thomas A rate-independent gradient system in damage coupled with plasticity via structured strains ESAIM: ProcS Volume 54, 54-69, 2016 ( Preprint )
- A. Mielke, J. Naumann. Global-in-time existence of weak solutions to Kolmogorov's two-equation model of turbulence. Comptes Rendus Acad. Sci. Paris Ser. I, 353: 321-326, 2015.
- A. Mielke, T. Roubíček. Rate-Independent Systems: Theory and Application. Applied Mathematical Sciences, Volume 193, XXII+660 pages, New York: Springer 2015.
Last modified: 2022-01-17 by Artur Stephan