We study the convergence of sequences of nonlinear integrodifferential reaction-diffusion equations when the Fickian terms belong to a class of convex functionals defined on a Hilbert space, equipped with the Mosco-convergence, and the non Fickian terms belong to a class of convex functionals, whose restrictions to a compactly embedded subspace are equipped with the -convergence. As a consequence we prove a homogenization theorem for this class under a stochastic homogenization framework.
Mots clés : Integrodifferential diffusion equations, non Fickian flux, Mosco-convergence, $\Gamma $-convergence, Convergence of reaction-diffusion equations, stochastic homogenization
Omar Anza Hafsa 1 ; Jean Philippe Mandallena 1 ; Gérard Michaille 1
CC-BY 4.0
@article{AMBP_2022__29_1_1_0,
author = {Omar Anza Hafsa and Jean Philippe Mandallena and G\'erard Michaille},
title = {Convergence of nonlinear integrodifferential reaction-diffusion equations via {Mosco}$\times \Gamma $-convergence},
journal = {Annales math\'ematiques Blaise Pascal},
pages = {1--50},
publisher = {Universit\'e Clermont Auvergne, Laboratoire de math\'ematiques Blaise Pascal},
volume = {29},
number = {1},
year = {2022},
doi = {10.5802/ambp.406},
language = {en},
url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.406/}
}
TY - JOUR AU - Omar Anza Hafsa AU - Jean Philippe Mandallena AU - Gérard Michaille TI - Convergence of nonlinear integrodifferential reaction-diffusion equations via Mosco$\times \Gamma $-convergence JO - Annales mathématiques Blaise Pascal PY - 2022 SP - 1 EP - 50 VL - 29 IS - 1 PB - Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal UR - https://ambp.centre-mersenne.org/articles/10.5802/ambp.406/ DO - 10.5802/ambp.406 LA - en ID - AMBP_2022__29_1_1_0 ER -
%0 Journal Article %A Omar Anza Hafsa %A Jean Philippe Mandallena %A Gérard Michaille %T Convergence of nonlinear integrodifferential reaction-diffusion equations via Mosco$\times \Gamma $-convergence %J Annales mathématiques Blaise Pascal %D 2022 %P 1-50 %V 29 %N 1 %I Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal %U https://ambp.centre-mersenne.org/articles/10.5802/ambp.406/ %R 10.5802/ambp.406 %G en %F AMBP_2022__29_1_1_0
Omar Anza Hafsa; Jean Philippe Mandallena; Gérard Michaille. Convergence of nonlinear integrodifferential reaction-diffusion equations via Mosco$\times \Gamma $-convergence. Annales mathématiques Blaise Pascal, Tome 29 (2022) no. 1, pp. 1-50. doi : 10.5802/ambp.406. https://ambp.centre-mersenne.org/articles/10.5802/ambp.406/
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