Convergence of nonlinear integrodifferential reaction-diffusion equations via Mosco×Γ-convergence
Annales mathématiques Blaise Pascal, Volume 29 (2022) no. 1, pp. 1-50.

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 Γ-convergence. As a consequence we prove a homogenization theorem for this class under a stochastic homogenization framework.

Published online:
DOI: 10.5802/ambp.406
Classification: 35K57, 35B27, 35R60, 45K05, 49K45
Keywords: 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

1 Université de Nîmes, Laboratoire MIPA Site des Carmes Place Gabriel Péri 30021 Nîmes FRANCE
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Omar Anza Hafsa; Jean Philippe Mandallena; Gérard Michaille. Convergence of nonlinear integrodifferential reaction-diffusion equations via Mosco$\times \Gamma $-convergence. Annales mathématiques Blaise Pascal, Volume 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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