无界域上非自治随机反应扩散方程一致随机吸引子的存在性  

Existence of Uniform Random Attractor for Nonautonomous Stochastic Reaction-diffusion Equations on Unbounded Domains

作　　者：张杰 李晓军[1] ZHANG Jie;LI Xiaojun(School of Science,Hehai University,Nanjing Jiangsu 210098,China)

机构地区：[1]河海大学理学院,江苏南京210098

出　　处：《广西师范大学学报（自然科学版）》2020年第2期134-143,共10页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(11571092)。

摘　　要：本文研究无界域上一类带有白噪声的非自治随机反应扩散方程一致吸引子的存在性。首先通过对解的一致估计,证明了对应于原方程的随机动力系统拥有关于符号空间的一致拉回吸收集;其次,通过渐近尾部估计得到解是一致拉回渐近紧性,从而得到原系统一致随机吸引子的存在性。This paper studies the existence of uniform attractors for a class of nonautonomous stochastic reaction-diffusion equations with white noise on unbounded domains. Firstly, with uniform estimation of the solutions, it is proved that the stochastic dynamical system corresponding to the original equation has a uniformly with respect to symbol space pullback absorbing set. Secondly, by asymptotic tail estimation, it is proved that the solution is uniformly pullback and asymptotically compact. The existence of uniform random attractor of the original system is obtained.

关 键 词：随机反应扩散方程 一致吸引子 无界域 白噪声 渐近紧性 

分 类 号：O175.29[理学—数学]