一类非自治随机波动方程的随机吸引子  

The Random Attractors of a Class of Non-autonomous Stochastic Wave Equations

作　　者：文慧霞 舒级[1] 李林芳 WEN Huixia;SHU Ji;LI Linfang(College of Mathematics and Software Science,Sichuan Normal University,Chengdu 610066,Sichuan)

机构地区：[1]四川师范大学数学与软件科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2019年第2期168-175,共8页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11371267和11571245);四川省科技厅应用基础计划项目(2016JY0204)

摘　　要：考虑带加性噪声的非自治随机波动方程在R3的有界区域D上的渐近行为.首先将随机偏微分方程转化为仅含随机参数的随机方程,然后运用解的一致估计方法证明随机吸收集的存在性,进一步利用压缩函数方法获得渐近紧性,最后得到随机动力系统拉回吸引子的存在性.In this paper,we study the asymptotic behavior of non-autonomous stochastic wave equations with additive noise on a bounded domain D■R^3.Firstly,the partial differential equation is transfromed into the random equation that only includes the ran-dom parameters.Then the existence of pullback absorbing set is proved by uniform estimates of solution method.Moreover,from con-structing contractive functions,asymptotic compactness is obtained.Finally,the existence of random attractor is given.

关 键 词：非自治随机波动方程 随机动力系统 拉回吸引子 加性噪声 

分 类 号：O175.29[理学—数学]