Wong–Zakai approximations and random attractors of non-autonomous stochastic discrete complex Ginzburg–Landau equations

2021 ◽  
Vol 62 (6) ◽  
pp. 062701
Author(s):  
Yuan Yang ◽  
Ji Shu ◽  
Xiaohu Wang
Keyword(s):  
Ginzburg Landau ◽  
Random Attractors ◽  
Ginzburg Landau Equations ◽  
Discrete Complex

Wong–Zakai approximations and limiting dynamics of stochastic Ginzburg–Landau equations

2021 ◽  
Author(s):  
Ji Shu ◽  
Dandan Ma ◽  
Xin Huang ◽  
Jian Zhang
Keyword(s):  
White Noise ◽  
Landau Equation ◽  
Upper Semicontinuity ◽  
Approximate Equation ◽  
Ginzburg Landau ◽  
Random System ◽  
Additive White Noise ◽  
Random Attractors ◽  
Ginzburg Landau Equations ◽  
Weaker Conditions

This paper deals with the Wong–Zakai approximations and random attractors for stochastic Ginzburg–Landau equations with a white noise. We first prove the existence of a pullback random attractor for the approximate equation under much weaker conditions than the original stochastic equation. In addition, when the stochastic Ginzburg–Landau equation is driven by an additive white noise, we establish the convergence of solutions of Wong–Zakai approximations and the upper semicontinuity of random attractors of the approximate random system as the size of approximation tends to zero.

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