The Cocycle for the Non-autonomous Stochastic Damped Wave Equations with White Noises
Article Sidebar
Published
Jul 6, 2019
Page:
1-8
Main Article Content
Hongyan Li
College of Management, Shanghai University of Engineering Science, Shanghai 201620, P. R. China.
Abstract
This paper is devoted to the cocycle of solutions of the non-autonomous stochastic damped wave equations with multiplicative white noises defined on unbounded domains. And we obtain the existence of a pullback absorbing set of the cocycle in a certain parameter region.
Keywords:
Stochastic damped wave equations, cocycle, pullback absorbing set.
Article Details
How to Cite
Section
Original Research Article
References
Arnold L. Random dynamical systems. Springer Monographs in Mathematics, Springer-Verlag, Berlin; 1998.
Fan X. Attractors for a damped stochastic wave equation of sine-Gordon type with sublinear multiplicative noise. Stochastic Analysis and Applications. 2006;24:767-793.
Lv Y, Wang W. Limiting dynamics for stochastic wave equations. Journal Dierential Equations. 2008;244:1-23.
Caraballo T, Lukaszewicz G, Real J. Pullback attractors for asymptotically compact nonautonomous dynamical systems. Nonlinear Analysis: Theory, Methods and Applications. 2006;64:484-498.
Jones R, Wang B. Asymptotic behavior of a class of stochastic nonlinear wave equations with dispersive and dissipative terms.Nonlinear Analysis: Real World Applications. 2013;14:1308-1322.
Wang ZJ, Zhou S, Gu AH. Random attractor of the stochastic strongly damped wave equation. Commun. Nonlinear. Sci. Numer. Simulat. 2012;17:1649-1658.
Li H, You Y. Random attractor for stochastic wave equation with arbitrary exponent and additive noise on Rn. Dynamics of PDE. 2015;12:343-378.
Wang B, Random attractors for non-autonomous stochasitic wave equations with multiplicative noise. Discrete and Continuous Dynamical Systems. 2014;34(1):269-300.
Wang Z, Zhou S, Gu A. Random attractor for a stochastic damped wave equation with multiplicative noise on unbounded domains. Nonlinear Analysis: Real World Applications. 2011;12:3468-3482.
Li H, You Y, Tu J, Random attractors and averaging for non-autonomous stochastic wave equations with nonlinear damping. J. Dierential Equations. 2015;258:148-190.
Fan X. Attractors for a damped stochastic wave equation of sine-Gordon type with sublinear multiplicative noise. Stochastic Analysis and Applications. 2006;24:767-793.
Lv Y, Wang W. Limiting dynamics for stochastic wave equations. Journal Dierential Equations. 2008;244:1-23.
Caraballo T, Lukaszewicz G, Real J. Pullback attractors for asymptotically compact nonautonomous dynamical systems. Nonlinear Analysis: Theory, Methods and Applications. 2006;64:484-498.
Jones R, Wang B. Asymptotic behavior of a class of stochastic nonlinear wave equations with dispersive and dissipative terms.Nonlinear Analysis: Real World Applications. 2013;14:1308-1322.
Wang ZJ, Zhou S, Gu AH. Random attractor of the stochastic strongly damped wave equation. Commun. Nonlinear. Sci. Numer. Simulat. 2012;17:1649-1658.
Li H, You Y. Random attractor for stochastic wave equation with arbitrary exponent and additive noise on Rn. Dynamics of PDE. 2015;12:343-378.
Wang B, Random attractors for non-autonomous stochasitic wave equations with multiplicative noise. Discrete and Continuous Dynamical Systems. 2014;34(1):269-300.
Wang Z, Zhou S, Gu A. Random attractor for a stochastic damped wave equation with multiplicative noise on unbounded domains. Nonlinear Analysis: Real World Applications. 2011;12:3468-3482.
Li H, You Y, Tu J, Random attractors and averaging for non-autonomous stochastic wave equations with nonlinear damping. J. Dierential Equations. 2015;258:148-190.