Random attractors for the stochastic coupled fractional Ginzburg-Landau equation with additive noise

2015 ◽  
Vol 56 (10) ◽  
pp. 102702 ◽  
Author(s):  
Ji Shu ◽  
Ping Li ◽  
Jia Zhang ◽  
Ou Liao
Keyword(s):  
Additive Noise ◽  
Landau Equation ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Random Attractors

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 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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