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Random attractors for wave equations on unbounded domains

Pages: 800 - 809, Issue Special, September 2009

 Abstract        Full Text (172.3K)              

Bixiang Wang - Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM 87801, United States (email)
Xiaoling Gao - Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM 87801, United States (email)

Abstract: The asymptotic behavior of stochastic wave equations on $\mathbb{R}^n$ is studied. The existence of a random attractor for the corresponding random dynamical system in $H^1(\mathbb{R}^n) \times L^2(\mathbb{R}^n)$ is established, where the nonlinearity has an arbitrary growth order for $n \le 2$ and is subcritical for $n=3$.

Keywords:  Random attractor, asymptotic compactness, wave equation
Mathematics Subject Classification:  Primary: 37L55; Secondary: 60H15, 35B40

Received: July 2008;      Revised: April 2009;      Published: September 2009.