Random Attractors for Delay Parabolic Equations with Additive Noise and Deterministic Nonautonomous Forcing

Abstract

In this paper, we consider the long term behavior of solutions to stochastic delay parabolic equations with additive noise and deterministic nonautonomous forcing. We first establish the existence of a continuous nonautonomous random dynamical system for the equations. Then we prove pullback asymptotical compactness of solutions as well as the existence and uniqueness of tempered random attractors. Finally, we establish the upper semicontinuity of the random attractors when noise intensity and time delay approach zero, respectively.