Stability of a class of nonlinear reaction–diffusion equations and stochastic homogenization

Article type: Research Article

Authors: Anza Hafsa, Omar | Mandallena, Jean Philippe | Michaille, Gérard^{; *}

Affiliations: Laboratoire MIPA, Universite de Nimes, Site des Carmes, Place Gabriel Péri, 30021 Nîmes, France. E-mails: omar.anza-hafsa@unimes.fr, jean-philippe.mandallena@unimes.fr, gerard.michaille@gmail.com

Correspondence: [*] Corresponding author. E-mail: gerard.michaille@gmail.com.

Abstract: We establish a convergence theorem for a class of nonlinear reaction–diffusion equations when the diffusion term is the subdifferential of a convex functional in a class of functionals of the calculus of variations equipped with the Mosco-convergence. The reaction term, which is not globally Lipschitz with respect to the state variable, gives rise to bounded solutions, and cover a wide variety of models. As a consequence we prove a homogenization theorem for this class under a stochastic homogenization framework.

Keywords: Convergence of reaction–diffusion equations, stochastic homogenization, comparison principle

DOI: 10.3233/ASY-191531

Journal: Asymptotic Analysis, vol. 115, no. 3-4, pp. 169-221, 2019