Dynamics of a Class of Stochastic Parabolic Equations with Delay and Non-Autonomous Forcing

This paper is concerned with the dynamics of solutions of a class of stochastic parabolic equations with delay and deterministic non-autonomous forcing. Specifically, the existence of random attractors is proven, and the upper semicontinuity of random attractors is shown when the delay approaches zero. The key technique in the proof of the existence results of random attractors is to derive some uniform estimates of solutions, and the most important step in the proof of the upper semicontinuity of random attractors is to establish the convergence of solutions.