Long term behavior of stochastic discrete complex Ginzburg-Landau equations with time delays in weighted spaces

Dingshi Li; Lin Shi; Xiaohu Wang

doi:10.3934/dcdsb.2019046

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2019, Volume 24, Issue 9: 5121-5148. Doi: 10.3934/dcdsb.2019046

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Long term behavior of stochastic discrete complex Ginzburg-Landau equations with time delays in weighted spaces

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: August 31, 2018

Early access: February 2019

Published: July 2019

This work was supported by NSFC (11331007, 11601446, 11701475 and 11871049) and Excellent Youth Scholars of Sichuan University (2016SCU04A15)

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Abstract

In this paper, we investigate the long term behavior of the solutions to a class of stochastic discrete complex Ginzburg-Landau equations with time-varying delays and driven by multiplicative white noise. We first prove the existence and uniqueness of random attractor in a weighted space for these equations. Then, we analyze the upper semicontinuity of the random attractors as the time delay approaches to zero.

Keywords:

Discrete complex Ginzburg-Landau equation,
delay,
random attractor,
weighted spaces.

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

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