Pullback Measure Attractors for Non-autonomous Fractional Stochastic Reaction-Diffusion Equations on Unbounded Domains

Abstract

This paper is concerned with the pullback measure attractors of the non-autonomous fractional reaction-diffusion equations defined on \(\mathbb {R}^{n}\). We first prove the existence and uniqueness of pullback measure attractors for such equations. Then we establish the upper semi-continuity of these attractors as the noise intensity \(\varepsilon \) tends to zero. Specifically, we apply the uniform estimates on the tails of solutions to prove the asymptotic compactness of a family of probability distributions of solutions to overcome the non-compactness of usual Sobolev embeddings on unbounded domains.