无界域上非自治随机强阻尼波动方程的一致随机吸引子的存在性  

Existence of Uniform Random Attractor for Non-autonomous Stochastic Strongly Damped Wave Equation on Unbounded Domains

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

机构地区：[1]河海大学理学院

出　　处：《河北师范大学学报（自然科学版）》2020年第1期6-17,共12页Journal of Hebei Normal University：Natural Science

基　　金：国家自然科学基金(11571092)

摘　　要：研究了无界域上一类带有可加白噪声的随机波动方程一致吸引子的存在性.首先,通过对变换系统解的一致估计,证明对应于原方程的随机动力系统拥有关于符号空间一致的拉回吸收集.其次,通过渐近尾部估计得到解是一致拉回渐近紧的,从而得到原系统一致随机吸引子的存在性.In this paper,we study the existence of uniform attractors for a class of nonautonomous stochastic strongly damped wave equations with additive white noise on unbounded domains.First,by using the uniform estimates of solutions of transformed system,we prove that the stochastic dynamical system corresponding to the original equation has a uniformly pullback absorbing set.Second,by asymptotic tail estimation,we obtain that the solution is uniformly pullback asymptotically compact.The existence of uniform random attractor of the original system is obtained.

关 键 词：强阻尼 波动方程 一致随机吸引子 无界域 

分 类 号：O175.2[理学—数学]