Attractors for non-autonomous parabolic problems with singular initial data

Abstract: In this paper, we study the asymptotic behavior of solutions of non-autonomous parabolic problems with singular initial data. We first establish the well-posedness of the equation when the initial data belongs to () and (), respectively. When the initial data belongs to , we establish the existence of uniform attractors in for the family of processes with external forces being translation bounded but not translation compact in . When we consider the existence of uniform attractors in , the solution of equation lacks the higher regularity, so we introduce a new type of solution and prove the existence result. For the long time behavior of solutions of the equation in , we only obtain the uniform attracting property in the weak topology. [Copyright &y& Elsevier]