无界域上一类带白噪声随机反应扩散方程的动力学行为

Dynamic Behavior for a Class of Stochastic Reaction-Diffusion Equations with White Noise on Unbounded Domains

研究无界域上一类带白噪声的随机反应扩散方程随机吸引子的存在性.通过对解的估计与渐近先验估计,说明对应于原方程的随机动力系统拥有一随机吸收集,且在拉回意义下是渐近紧的,从而得到原系统随机吸引子的存在性.

We focus on the existence of random attractor for a class of stochastic reaction-diffusion equations with white noise on unbounded domains.By estimate and asymptotic a prior estimate of solutions,we illustrate the random dynamic system of the original equation has a random absorbing set,which is asymptotically compact in the sense of pullback.Then the existence of random attractor of original system is obtained.