scholarly journals Asymptotic behavior of random coupled Ginzburg-Landau equation driven by colored noise on unbounded domains

2020 ◽  
Author(s):  
Zhang Chen ◽  
Lingyu Li ◽  
Dan Yang
Keyword(s):  
Asymptotic Behavior ◽  
Colored Noise ◽  
Landau Equation ◽  
Unbounded Domains ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation

scholarly journals Asymptotic behavior of random coupled Ginzburg–Landau equation driven by colored noise on unbounded domains

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Zhang Chen ◽  
Lingyu Li ◽  
Dandan Yang
Keyword(s):  
Asymptotic Behavior ◽  
Lipschitz Condition ◽  
Colored Noise ◽  
Nonlinear Term ◽  
Coupling Parameter ◽  
Landau Equation ◽  
Unbounded Domains ◽  
Ginzburg Landau ◽  
Local Lipschitz Condition ◽  
Ginzburg Landau Equation

AbstractIn this paper, a random coupled Ginzburg–Landau equation driven by colored noise on unbounded domains is considered, in which the nonlinear term satisfies a local Lipschitz condition. It is shown that the random attractor of such a coupled Ginzburg–Landau equation is a singleton set, and the components of solutions are very close when the coupling parameter becomes large enough.

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.

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