Limiting behavior of non-autonomous stochastic reaction–diffusion equations on thin domains

Abstract

This paper deals with the limiting behavior of stochastic reaction–diffusion equations driven by multiplicative noise and deterministic non-autonomous terms defined on thin domains. We first prove the existence, uniqueness and periodicity of pullback tempered random attractors for the equations in an (n+1)-dimensional narrow domain, and then establish the upper semicontinuity of these attractors when a family of (n+1)-dimensional thin domains collapses onto an n-dimensional domain.