Existence and upper semicontinuity of random attractors for non-autonomous stochastic strongly damped wave equation with multiplicative noise

Zhaojuan Wang; Shengfan Zhou

doi:10.3934/dcds.2017120

Article Contents

2017, Volume 37, Issue 5: 2787-2812. Doi: 10.3934/dcds.2017120

This issue Previous Article The existence of nontrivial solutions to Chern-Simons-Schrödinger systems Next Article Monotonicity and uniqueness of wave profiles for a three components lattice dynamical system

Existence and upper semicontinuity of random attractors for non-autonomous stochastic strongly damped wave equation with multiplicative noise

Zhaojuan Wang^1, , and
Shengfan Zhou^2,

1.
School of Mathematical Science, Huaiyin Normal University, Huaian, 223300, China
2.
Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

* Corresponding author: Zhaojuan Wang
* Corresponding author: Zhaojuan Wang

Received: June 30, 2016

Revised: December 31, 2016

Published: May 2017

The authors are supported by NSFC grant No. 11326114, 11401244, 11471290. Natural Science Research Project of Ordinary Universities in Jiangsu Province grant No. 14KJB110003. Zhejiang Natural Science Foundation grant No. LY14A010012 and Zhejiang Normal University Foundation grant No. ZC304014012.

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Abstract

In this paper we study the asymptotic behavior of solutions of the non-autonomous stochastic strongly damped wave equation driven by multiplicative noise defined on unbounded domains. We first introduce a continuous cocycle for the equation. Then we consider the existence of a tempered pullback random attractor for the cocycle. Finally we establish the upper semicontinuity of random attractors as the coefficient of the white noise term tends to zero.

Keywords:

Stochastic strongly damped wave equation,
unbounded domains,
random attractor,
upper semicontinuity.

Mathematics Subject Classification: Primary: 37L55; Secondary: 35B41, 35B40.

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