Dynamics of the non-autonomous stochastic p-Laplacian parabolic problems on unbounded thin domains

Abstract

This paper focuses on the dynamics of the non-autonomous stochastic p-Laplacian parabolic problems defined on unbounded thin domains. We first show that the tails of solutions of the equation are uniformly small outside a bounded domain, which is utilized to overcome the non-compactness of Sobolev embeddings on unbounded domains. We then prove the existence and uniqueness of random attractors for the equations defined on (n + 1)-dimensional unbounded thin domains and further establish the upper semi-continuity of attractors as the thin domains collapse onto the space Rn.