Asymptotic Behavior of Non-autonomous Random Ginzburg–Landau Equations with Colored Noise on Unbounded Thin Domains

Abstract

This paper is mainly concerned with non-autonomous random complex Ginzburg–Landau equations with nonlinear multiplicative colored noise on unbounded thin domains. Together with the properties of the colored noise, uniform estimates of solutions for such random equations are derived. Moreover, the pullback asymptotic compactness is proved by the tail-estimates method, and the existence and uniqueness of pullback attractors are further obtained. In addition, when the unbounded thin domain collapses onto the real space ℝ, the upper semi-continuity of pullback attractors is also investigated.

Keywords

Non-autonomous random Ginzburg–Landau equation / colored noise / unbounded thin domain / pullback attractor / upper semi-continuity