Random Attractor for Stochastic Wave Equation with Arbitrary Exponent and Additive Noise on $\mathbb{R}^n$

摘要

Asymptotic random dynamics of weak solutions for a damped stochastic waveequation with the nonlinearity of arbitrarily large exponent and the additivenoise on $\mathbb{R}^n$ is investigated. The existence of a pullback randomattractor is proved in a parameter region with a breakthrough in proving thepullback asymptotic compactness of the cocycle with the quasi-trajectoriesdefined on the integrable function space of arbitrary exponent and on theunbounded domain of arbitrary dimension.