Dynamics for the Stochastic Plate Equations of Kirchhoff Type on $\mathbb{R}^n$

Abstract

In this paper, we study mainly the long-time behavior of the stochastic plate equations of kirchhoff type with nonlinear damping on unbounded domains. Due to the lack of compactness of Sobolev embeddings on unbounded domains, pullback asymptotic compactness of cocycle associated with the system is proved by the tail-estimates method and splitting technique.