Article Contents

2014, Volume 34, Issue 1: 269-300. Doi: 10.3934/dcds.2014.34.269

This issue Previous Article Frequency domain conditions for finite-dimensional projectors and determining observations for the set of amenable solutions Next Article Random attractors and robustness for stochastic reversible reaction-diffusion systems

Random attractors for non-autonomous stochastic wave equations with multiplicative noise

Bixiang Wang^1,

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

Received: October 2012

Revised: February 2013

Published: January 2014

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Abstract

This paper is concerned with the asymptotic behavior of solutions of the damped non-autonomous stochastic wave equations driven by multiplicative white noise. We prove the existence of pullback random attractors in $H^1(\mathbb{R}^n) \times L^2(\mathbb{R}^n)$ when the intensity of noise is sufficiently small. We demonstrate that these random attractors are periodic in time if so are the deterministic non-autonomous external terms. We also establish the upper semicontinuity of random attractors when the intensity of noise approaches zero. In addition, we prove the measurability of random attractors even if the underlying probability space is not complete.

Keywords:

Mathematics Subject Classification: Primary: 35B40; Secondary: 35B41, 37L30.

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