Asymptotic behavior for a stochasticwave equation with dynamical boundary conditions

Guanggan Chen; Jian Zhang

doi:10.3934/dcdsb.2012.17.1441

Article Contents

2012, Volume 17, Issue 5: 1441-1453. Doi: 10.3934/dcdsb.2012.17.1441

This issue Previous Article A mathematical and numerical analysis of the Maxwell-Stefan diffusion equations Next Article The Euler-Maruyama approximation for the absorption time of the CEV diffusion

Asymptotic behavior for a stochastic wave equation with dynamical boundary conditions

Guanggan Chen^1, and
Jian Zhang^2,

1.
College of Mathematics and Software Science, Sichuan Normal University, Chengdu, 610068
2.
College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610068

Received: June 2011

Revised: February 2012

Published: July 2012

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Abstract

This work is concerned with the asymptotic dynamical behavior for a weakly damped stochastic nonlinear wave equation with dynamical boundary conditions. The white noises appear both in the model and in the dynamical boundary condition. Since the energy relation of this stochastic system does not directly imply the a priori estimate of the solution, we propose a pseudo energy equation to infer almost sure boundedness of the solution. Then a unique invariant measure is shown to exist for the system.

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Mathematics Subject Classification: Primary: 60H15, 37H05, 37L55, 37L25; Secondary: 37D10.

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