Homogenization of Attractors of Reaction–Diffusion System with Rapidly Oscillating Terms in an Orthotropic Porous Medium

Abstract

In a perforated domain, we consider a reaction-diffusion system with rapidly oscillating terms in the equations and boundary conditions. No Lipschitz condition is imposed, so the uniqueness of a solution to the corresponding initial-boundary value problem is not guaranteed. We prove that the trajectory attractors of the system weakly converge to the trajectory attractors of the homogenized reaction-diffusion systems with a strange term (potential).