Parabolic equations with localized large diffusion: Rate of convergence of attractors

Abstract

In this paper we study the asymptotic nonlinear dynamics of scalar semilinear parabolic problems of reaction-diffusion type when the diffusion coefficient becomes large in a subregion in the interior to the domain. We obtain, under suitable assumptions, that the family of attractors behaves continuously and we exhibit the rate of convergence. An accurate description of the localized large diffusion is necessary.