Convergence of nonlinear integrodifferential reaction-diffusion equations via Mosco$\times \Gamma$-convergence

Anza Hafsa, Omar; Mandallena, Jean Philippe; Michaille, Gérard

Annales mathématiques Blaise Pascal, Tome 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 $\Gamma$-convergence. As a consequence we prove a homogenization theorem for this class under a stochastic homogenization framework.

Classification : 35K57, 35B27, 35R60, 45K05, 49K45
Mots clés : Integrodifferential diffusion equations, non Fickian flux, Mosco-convergence, $\Gamma $-convergence, Convergence of reaction-diffusion equations, stochastic homogenization

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