Abstract
Abstract In this paper, we investigate the dynamics of stochastic plate equations with memory in unbounded domains. More specifically, we obtain the uniform time estimates for solutions of the problem. Based on the estimates above, we prove the existence and uniqueness of random attractors in unbounded domains.
Highlights
Let (Ω, ) be the standard probability space, where Ω = {ω ∈ C(, ) : ω(0) = 0}, is the Borel σ-algebra induced by the compact open topology of Ω, and is the Wiener measure on (Ω, )
There is a classical group {θt}t∈ acting on (Ω, ), which is defined by θtω(⋅) = ω(⋅ +t) − ω(t), for all ω ∈ Ω, t ∈, (Ω, {θt}t∈ ) is an ergodic parametric dynamical system
Many studies have been carried out regarding the dynamics of a variety of systems related to equation (1.1)
Summary
Considering the following non-autonomous stochastic plate equation with memory and multiplicative noise in unbounded domain n:. Motivated by the literature above, we investigate the asymptotic behaviors for stochastic plate equation driven by multiplicative noise in unbounded domains in this paper. These additional terms involve the unknown variable u and have great effect on the way to derive uniform estimates of solutions. This is the reason why, in this paper, we only study the existence of random attractors for the stochastic equation (1.1) when the intensity ε of the multiplicative noise is sufficiently small.
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