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

Abstract

We establish a convergence theorem for a class of two components nonlinear reactiondiffusion 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.