无界域上具有乘积噪声的随机反应-扩散方程一致随机吸引子的存在性

Existence of Uniform Random Attractors for Stochastic Reaction Diffusion Equations with Multiplicative Noise on Unbounded Domain

本文旨在研究无界区域上带有乘性噪声的随机反应扩散方程一致吸引子的存在性.首先利用Ornstein-Uhlenbeck过程,将原方程转化为一个非自治随机动力系统.之后,通过对解的一致估计,得到对应随机动力系统一致拉回随机吸收集的存在性.最后,通过渐近尾部估计,来得到解的一致拉回渐近紧性,从而得到一致随机吸引子的存在性.

In this paper,the existence of uniform random attractor has been investigated for stochastic reaction-diffusion equation with multiplicative noise on unbounded domain.Firstly,the original equation has been transformed into a nonautonomous stochastic dynamical system by using the Ornstein-Uhlenbeck process.Then,by uniformly estimating the solutions,the existence of uniform pullback random absorption set for the corresponding stochastic dynamical system has been obtained.Finally,the asymptotic tail estimation is used to obtain the uniformly pullback asymptotic compactness of the solution,and the existence of uniformly random attractors been obtained.