Attractors for parabolic problems in weighted spaces

Abstract

The purpose of this paper is to investigate the asymptotic behavior of the solutions of parabolic equations with singular initial data in weighted spaces L^r_{\delta(x)}(\Omega) where \delta(x) is the distance to the boundary. We first establish the existence of the attractor for that equation in L^r_{\delta(x)}(\Omega) and then show the existence of the exponential attractor in L^2_{\delta(x)}(\Omega). In contrast to our previous results, we get the existence of attractors in weak topology spaces.