Asymptotic behavior of non-autonomous random Ginzburg-Landau equation driven by colored noise

Abstract

<p style='text-indent:20px;'>This paper investigates mainly the long term behavior of the non-autonomous random Ginzburg-Landau equation driven by nonlinear colored noise on unbounded domains. Due to the noncompactness of Sobolev embeddings on unbounded domains, pullback asymptotic compactness of random dynamical system associated with such random Ginzburg-Landau equation is proved by the tail-estimates method. Moreover, it is proved that the pullback random attractor of the non-autonomous random Ginzburg-Landau equation driven by a linear multiplicative colored noise converges to that of the corresponding stochastic system driven by a linear multiplicative white noise.