Dynamics of Stochastic Ginzburg-Landau Equations Driven by Colored Noise on Thin Domains

Abstract

This work is concerned with the asymptotic behaviors of solutions to a class of non-autonomous stochastic Ginzburg-Landau equations driven by colored noise and deterministic non-autonomous terms defined on thin domains. The existence and uniqueness of tempered pullback random attractors are proved for the stochastic Ginzburg-Landau systems defined on $(n + 1)$-dimensional narrow domain. Furthermore, the upper semicontinuity of these attractors is established, when a family of $(n + 1)$-dimensional thin domains collapse onto an $n$-dimensional domain.