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.

scholarly journals Asymptotic behavior for non-autonomous stochastic plate equation on unbounded domains

2019 ◽  
Vol 17 (1) ◽  
pp. 1281-1302 ◽  
Author(s):  
Xiaobin Yao ◽  
Xilan Liu
Keyword(s):  
Asymptotic Behavior ◽  
Additive Noise ◽  
Upper Semicontinuity ◽  
Unbounded Domains ◽  
Asymptotic Behavior Of Solutions ◽  
Plate Equation ◽  
Uniform Estimates ◽  
Estimates Of Solutions ◽  
Random Attractors

Abstract We study the asymptotic behavior of solutions to the non-autonomous stochastic plate equation driven by additive noise defined on unbounded domains. We first prove the uniform estimates of solutions, and then establish the existence and upper semicontinuity of random attractors.

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 Modulation Equation for the Stochastic Swift–Hohenberg Equation with Cubic and Quintic Nonlinearities on the Real Line

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1217
Author(s):  
Wael W. Mohammed
Keyword(s):  
Unbounded Domain ◽  
Real Line ◽  
Additive Noise ◽  
Landau Equation ◽  
Ginzburg Landau ◽  
Modulation Equation ◽  
The Real ◽  
Quintic Nonlinearity ◽  
Ginzburg Landau Equation ◽  
Dominant Pattern

The purpose of this paper is to rigorously derive the cubic–quintic Ginzburg–Landau equation as a modulation equation for the stochastic Swift–Hohenberg equation with cubic–quintic nonlinearity on an unbounded domain near a change of stability, where a band of dominant pattern is changing stability. Also, we show the influence of degenerate additive noise on the stabilization of the modulation equation.

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