Pullback attractors of nonautonomous and stochastic multivalued dynamical systems

Abstract

In this paper we study the existence of pullback global attractors for multivalued processes generated by differential inclusions. First, we define multivalued dynamical processes, prove abstract results on the existence of !-limit sets and global attractors and study their topological properties (compactness, conectedness). Further, we apply the abstract results to nonautonomous differential inclusions of the reaction-diffusion type in which the forcing term can grow polynomially in time, and to stochastic differential inclusions as well.