Asymptotic behavior of a reaction-diffusion problem with delay and reaction term concentrated in the boundary

Abstract

In this work we analyze the asymptotic behavior of the solutions of a reaction-diffusion problem with delay when the reaction term is concentrated in a neighborhood of the boundary and this neighborhood shrinks to boundary, as a parameter goes to zero. This analysis of the asymptotic behavior uses, as a main tool, the convergence result found in [3]. Here, we prove the existence of a family of global attractors and that this family is upper semicontinuous at = 0. We also prove the continuity of the set of equilibria at = 0.