Asymptotic behavior of stochastic complex Ginzburg-Landau equations with deterministic non-autonomous forcing on thin domains

Dingshi Li; Xiaohu Wang

doi:10.3934/dcdsb.2018181

Article Contents

2019, Volume 24, Issue 2: 449-465. Doi: 10.3934/dcdsb.2018181

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Asymptotic behavior of stochastic complex Ginzburg-Landau equations with deterministic non-autonomous forcing on thin domains

Dingshi Li^1, and
Xiaohu Wang^2, ,

1.
School of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan 610031, China
2.
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China

* Corresponding author: Xiaohu Wang, wangxiaohu@scu.edu.cn
* Corresponding author: Xiaohu Wang, wangxiaohu@scu.edu.cn

Received: October 31, 2017

Revised: December 31, 2017

Early access: May 2018

Published: January 2019

This work was supported by NSFC (11271270, 11601446 and 11331007) and Excellent Youth Scholars of Sichuan University (2016SCU04A15)

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Abstract

In this paper, we investigate the asymptotic behavior for non-autonomous stochastic complex Ginzburg-Landau equations with multiplicative noise on thin domains. For this aim, we first show that the existence and uniqueness of random attractors for the considered equations and the limit equations. Then, we establish the upper semicontinuity of these attractors when the thin domains collapse onto an interval.

Keywords:

Thin domain,
stochastic complex Ginzburg-Landau equation,
random attractor,
upper semicontinuity.

Mathematics Subject Classification: Primary: 35B40; Secondary: 35B41, 37L30.

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