Existence of Pullback Attractors for Pullback Asymptotically Compact Processes

Abstract

This paper is concerned with the existence of pullback attractors for evolution processes. Our aim is to provide results that extend the following results for autonomous evolution processes (semigroups) i) An autonomous evolution process which is bounded dissipative and asymptotically compact has a global attractor. ii) An autonomous evolution process which is bounded, point dissipative and asymptotically compact has a global attractor. The extension of such results requires the introduction of new concepts and brings up some important differences between the asymptotic properties of autonomous and nonautonomous evolution processes. An application is considered to damped wave problem with non-autonomous damping.