## Abstract and Applied Analysis

### Random Attractors for Stochastic Ginzburg-Landau Equation on Unbounded Domains

#### Abstract

We prove the existence of a pullback attractor in ${\mathbb{L}}^{2}$ $({\Bbb R}^{n})$ for the stochastic Ginzburg-Landau equation with additive noise on the entire n-dimensional space ${\Bbb R}^{n}$. 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 unique $\mathcal{D}$-random attractor, for which the asymptotic compactness is established by the method of uniform estimates on the tails of its solutions.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 428685, 12 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412277027

Digital Object Identifier
doi:10.1155/2014/428685

Mathematical Reviews number (MathSciNet)
MR3219371

Zentralblatt MATH identifier
07022375

#### Citation

Lu, Qiuying; Deng, Guifeng; Zhang, Weipeng. Random Attractors for Stochastic Ginzburg-Landau Equation on Unbounded Domains. Abstr. Appl. Anal. 2014 (2014), Article ID 428685, 12 pages. doi:10.1155/2014/428685. https://projecteuclid.org/euclid.aaa/1412277027

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