Abstract
In this paper, we consider the stochastic higher-order Kirchhoff-type equation with nonlinear strongly dissipation and white noise. We first deal with random term by using Ornstein-Uhlenbeck process and establish the wellness of the solution, then the existence of global random attractor are proved.
Highlights
In this paper, we consider the following stochastic strongly damped higherorder nonlinear Kirchhoff-type equation with white noise:
The random attractor is popularized for classic determine dynamical system of the global attractor
Global attractor of Kirchhofftype equations have been investigated by many authors, see, e.g., [1] [2] [3] [4], the existence random attractor has been studied by many authors, in [5], Zhaojuan Wang, Shengfan Zhou and Anhui Gu, they study the asymptotic dynamics for a stochastic damped wave equation with multiplicative noise defined on unbounded domains, and investigate the existence of a random attractor, they overcome the difficulty of lacking the compactness of Sobolev embedding in unbounded domains by the energy equation
Summary
We collect some basic knowledge about general random dynamical system ([9] [10] [11]). 3) A random set B (ω ) is said to be a random absorbing set if for any tempered random set D (ω ) , and P − a.e. ω ∈ Ω , there exists t0 (ω ) such that φ (t,θ−tω, D (θ−tω )) ⊂ B (ω ) for all t ≥ t0 (ω ) . 6) A random compact set A(ω ) is said to be a random attractor if it is a random attracting set and φ (t,ω, A(ω )) = A(θtω ) for P − a.e. ω ∈ Ω and all t ≥0. ([10]) Let φ be a continuous random dynamical system with ( ) state space X over Ω, F, P,(θt )t∈R. A(ω ) is the unique random attractor of φ
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