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

Lingyu Li; Zhang Chen

doi:10.3934/dcdsb.2020233

Article Contents

2021, Volume 26, Issue 6: 3303-3333. Doi: 10.3934/dcdsb.2020233

This issue Previous Article Dynamic observers for unknown populations Next Article Entropy-dissipating finite-difference schemes for nonlinear fourth-order parabolic equations

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

Lingyu Li and
Zhang Chen^,

School of Mathematics, Shandong University, Jinan 250100, China

^* Corresponding author: Zhang Chen
^* Corresponding author: Zhang Chen

Received: November 2019

Revised: May 2020

Early access: August 2020

Published: June 2021

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Abstract

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.

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Mathematics Subject Classification: Primary: 60H15, 35B40, 35B41; Secondary: 35R60.

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