Perturbation of the diffusion and upper semicontinuity of attractors

We obtain uniform bounds for attractors of parabolic problems with nonlinea r boundary conditions with respect to perturbations in the diffusion coeffi cients. These bounds are the main tool to obtain continuity properties of t he attractors relatively to perturbations of the diffusion coefficient. We study two examples where the diffusion is perturbed: one related to homogen ization theory and the other taken from composite materials where the diffu sion goes to infinity in some subdomain. (C) 1999 Elsevier Science Ltd. All rights reserved.