# American Institute of Mathematical Sciences

June  2021, 26(6): 3303-3333. doi: 10.3934/dcdsb.2020233

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

 School of Mathematics, Shandong University, Jinan 250100, China

* Corresponding author: Zhang Chen

Received  November 2019 Revised  May 2020 Published  June 2021 Early access  August 2020

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.

Citation: Lingyu Li, Zhang Chen. Asymptotic behavior of non-autonomous random Ginzburg-Landau equation driven by colored noise. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3303-3333. doi: 10.3934/dcdsb.2020233
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