Publications of Dr. Martin Heida

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[P1]   Stochastic homogenization on randomly perforated domains. arXiv preprint 2001.10373, 2020.

[P2]   MH, M. Kantner, and A. Stephan. Consistency and convergence for a family of finite volume discretizations of the Fokker–Planck operator. WIAS preprint 2684, 2020.

Publications in refereed journals

[H25]   O. Souček , MH, and J. Málek. On a thermodynamic framework for developing boundary conditions for Korteweg fluids. International Journal of Engineering Science, 154, 2020.

[H24]   B. Franchi, MH, 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.

[H23]   MH, R. Kornhuber, and J. Podlesny. Fractal homogenization of multiscale interface problems. SIAM Multiscale Modeling and Simulation, 18(1):294–314, 2020.

[H22]   MH, S. Neukamm, and M. Varga. Stochastic homogenization of Λ-convex gradient flows. Accepted by Discrete and Continuous Dynamical Systems – S,, 2020.

[H21]   F. Flegel and MH. 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.

[H20]   F. Flegel, MH, and M. Slowik. Homogenization theory for the random conductance model with degenerate ergodic weights and unbounded-range jumps. Annales de l’Institut Henry Poincaré probabilités et statistiques, 55(3):1226–1257, 2019. (Preprint)

[H19]   MH and S. Nesenenko. Stochastic homogenization of rate-dependent models of monotone type in plasticity. Asymptotic Analysis, 112(3-4):185–212, 2019. (Preprint)

[H18]   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)

[H17]   MH and M. Röger. Large deviation principle for a stochastic Allen–Cahn equation. Journal of Theoretical Probability, 31(1):364–401, 2018. (Preprint)

[H16]   Convergences of the squareroot approximation scheme to the Fokker–Planck operator. Mathematical Models and Methods in Applied Sciences, 28(13):2599–2635, 2018. (Preprint)

[H15]   L. Donati, MH, 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)

[H14]   MH and B. Schweizer. Stochastic homogenization of plasticity equations. ESAIM: Control, Optimisation and Calculus of Variations, 24(1):153–176, 2018. (Preprint)

[H13]   C. Dörlemann, MH, and B. Schweizer. Transmission conditions for the Helmholtz-equation in perforated domains. Vietnam Journal of Mathematics, On the occasion of the 75th Birthday of W. Jäger, 45(1-2):241–253, 2017. (Preprint)

[H12]   Stochastic homogenization of rate-independent systems and applications. Continuum Mechanics and Thermodynamics, 29(3):853–894, 2017. (Preprint)

[H11]   MH and A. Mielke. Averaging of time-periodic dissipation potentials in rate-independent processes. Discrete & Continuous Dynamical Systems-Series S, 10(6), 2017. (Preprint)

[H10]   MH and B. Schweizer. Non-periodic homogenization of infinitesimal strain plasticity equations. ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 96(1):5–23, 2016. (Preprint)

[H09]   Existence of solutions for two types of generalized versions of the Cahn–Hilliard equation. Applications of Mathematics, 60(1):51–90, 2015. (Preprint)

[H08]   On systems of Cahn–Hilliard and Allen–Cahn equations considered as gradient flows in Hilbert spaces. Journal of Mathematical Analysis and Applications, 423(1):410–455, 2015. (Preprint)

[H07]   On thermodynamics of fluid interfaces. International Journal of Engineering Science, 82:178–195, 2014. (Preprint)

[H06]   On the derivation of thermodynamically consistent boundary conditions for the Cahn–Hilliard–Navier–Stokes system. International Journal of Engineering Science, 62:126–156, 2013. (Preprint)

[H05]   MH, J. Málek, and K. Rajagopal. On the development and generalizations of Allen–Cahn and Stefan equations within a thermodynamic framework. Zeitschrift für angewandte Mathematik und Physik, 63(4):759–776, 2012. (Preprint)

[H04]   MH, J. Málek, and K. R. Rajagopal. On the development and generalizations of Cahn–Hilliard equations within a thermodynamic framework. Zeitschrift für angewandte Mathematik und Physik, 63(1):145–169, 2012. (Preprint)

[H03]   Stochastic homogenization of heat transfer in polycrystals with nonlinear contact conductivities. Applicable Analysis, 91(7):1243–1264, 2012.

[H02]   An extension of the stochastic two-scale convergence method and application. Asymptotic Analysis, 72(1-2):1–30, 2011.

[H01]   MH and J. Málek. On compressible Korteweg fluid-like materials. International Journal of Engineering Science, 48(11):1313–1324, 2010. (Preprint)

PhD Thesis
Modeling Multiphase Flow in Porous Media with an Application to Permafrost Soil. (Access to full text.)

Diploma Thesis
Stochastic Homogenization of Heat Transfer through a Polycrystal,
University of Heidelberg, 2008.

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Last modified: 2018-04-08 by Martin Heida