Pullback attractors of non-autonomous stochastic degenerate parabolic equations on unbounded domains

This paper is concerned with pullback attractors of the stochastic p-Laplace equation defined on the entire space Rn. We first establish the asymptotic compactness of the equation in L2(Rn) and then prove the existence and uniqueness of non-autonomous random attractors. This attractor is pathwise periodic if the non-autonomous deterministic forcing is time periodic. The difficulty of non-compactness of Sobolev embeddings on Rn is overcome by the uniform smallness of solutions outside a bounded domain. © 2014 Elsevier Inc.