scholarly journals RANDOM ATTRACTORS FOR NON-AUTONOMOUS FRACTIONAL STOCHASTIC GINZBURG-LANDAU EQUATIONS ON UNBOUNDED DOMAINS

2020 ◽  
Vol 10 (6) ◽  
pp. 2592-2618
Author(s):  
Ji Shu ◽  
◽  
Jian Zhang ◽  
Keyword(s):  
Unbounded Domains ◽  
Ginzburg Landau ◽  
Random Attractors ◽  
Ginzburg Landau Equations

scholarly journals Random Attractors for Stochastic Ginzburg-Landau Equation on Unbounded Domains

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Qiuying Lu ◽  
Guifeng Deng ◽  
Weipeng Zhang
Keyword(s):  
Additive Noise ◽  
Dimensional Space ◽  
Landau Equation ◽  
Unbounded Domains ◽  
Random Dynamical System ◽  
Pullback Attractor ◽  
Ginzburg Landau ◽  
Uniform Estimates ◽  
Ginzburg Landau Equation ◽  
Random Attractors

We prove the existence of a pullback attractor inL2(ℝn)for the stochastic Ginzburg-Landau equation with additive noise on the entiren-dimensional spaceℝn. We show that the stochastic Ginzburg-Landau equation with additive noise can be recast as a random dynamical system. We demonstrate that the system possesses a uniqueD-random attractor, for which the asymptotic compactness is established by the method of uniform estimates on the tails of its solutions.

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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