Approximation of attractors for multivalued random dynamical systems

Abstract

The concept of global attractor for stochastic partial differential inclusions has been recently introduced as a joint generalization of the theory of random attractors for random dynamical systems and global attractors for multivalued semiflows. We present a general result on the upper semicontinuity of attractors for multivalued random dynamical systems. In particular, our theory shows how the random attractor associated to a small random perturbation of a (deterministic) partial differential inclusion approximates the global attractor of the limiting problem. Some applications ilustrate the results.