Stability of a class of nonlinear reaction–diffusion equations and stochastic homogenization
Omar Anza Hafsa, Jean-Philippe Mandallena, Gérard Michaille · Asymptotic Analysis · 2019
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.