Random attractors for wave equations on unbounded domains

Bixiang Wang; Xiaoling Gao

doi:10.3934/proc.2009.2009.800

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2009, Volume 2009: 800-809. Doi: 10.3934/proc.2009.2009.800 open access

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Random attractors for wave equations on unbounded domains

Bixiang Wang^1, and
Xiaoling Gao^1,

1.
Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM 87801

Received: June 30, 2008

Revised: March 31, 2009

Published: August 2009

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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 $n=3$.

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Mathematics Subject Classification: Primary: 37L55; Secondary: 60H15, 35B40.

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