Dynamics of Partial Differential Equations

Volume 12 (2015)

Number 4

Random attractor for stochastic wave equation with arbitrary exponent and additive noise on $\mathbb{R}^n$

Pages: 343 – 378

DOI: https://dx.doi.org/10.4310/DPDE.2015.v12.n4.a3


Hongyan Li (College of Management, Shanghai University of Engineering Science, Shanghai, China)

Yuncheng You (Department of Mathematics and Statistics, University of South Florida, Tampa, Fla., U.S.A.)


Asymptotic random dynamics of weak solutions for a damped stochastic wave equation with the nonlinearity of arbitrarily large exponent and the additive noise on $\mathbb{R}^n$ is investigated. The existence of a pullback random attractor is proved in a parameter region with a breakthrough in proving the pullback asymptotic compactness of the cocycle with the quasi-trajectories defined on the integrable function space of arbitrary exponent and on an unbounded domain of arbitrary space dimension.


stochastic wave equations, random dynamical system, random attractor, pullback asymptotic compactness, additive noise, arbitrary nonlinear exponents, unbounded domain

2010 Mathematics Subject Classification

Primary 35B40, 35B41, 35R60, 37L55. Secondary 60H15.

Published 10 December 2015