Convergence and stochastic homogenization of a class of two components nonlinear reaction–diffusion systems

Article type: Research Article

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

Affiliations: Universite de Nimes, Laboratoire MIPA, 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 two components nonlinear reaction–diffusion systems. Each diffusion term is the subdifferential of a convex functional of the calculus of variations whose class is equipped with the Mosco-convergence. The reaction terms are structured in such a way that the systems admit bounded solutions, which are positive in the modeling of ecosystems. As a consequence, under a stochastic homogenization framework, we prove two homogenization theorems for this class. We illustrate the results with the stochastic homogenization of a prey–predator model with saturation effect.

Keywords: Convergence of two components reaction–diffusion equations, stochastic homogenization, prey–predator models

DOI: 10.3233/ASY-201603

Journal: Asymptotic Analysis, vol. 121, no. 3-4, pp. 259-305, 2021