Attractors for a Class of Abstract Evolution Equations with Fading Memory

Abstract

In this paper, we study the dynamics of an abstract evolution equation with fading memory with a critical growing nonlinearity. By use of some new methods and asymptotic estimate techniques, we first verify the asymptotic compact of solution semigroup and then prove the existence of global attractors in weak topological space and strong topological space, while the forcing term only belongs to H-1(Ω) or L2(Ω), respectively. The results are new and appear to be optimal.