“Strange term” in homogenization of attractors of reaction–diffusion equation in perforated domain

Abstract

Abstract We consider reaction–diffusion equation in perforated domain, with rapidly oscillating coefficient in boundary conditions. We do not assume any Lipschitz condition for the nonlinear function in the equation, so, the uniqueness theorem for the corresponding initial boundary value problem may not hold for the considered reaction-diffusion equation. We prove that the trajectory attractors of this equation tend in a weak sense to the trajectory attractors of the homogenized reaction-diffusion equation with a “strange term” (potential). Bibliography: 48 titles.