一类由小噪声驱动的非自治随机波动方程的渐近行为  

Asymptotic behavior of a class of non-autonomous stochastic wave equation driven by small noise

作　　者：佘连兵 林荣瑞 徐冬梅 SHE Lian-bing;LIN Rong-rui;XU Dong-mei(School of Mathematics and Information Engineering,Liupanshui Normal University,Liupanshui,553004,China;School of Mathematics and Computer,Shangrao Normal University,Shangrao 334001,China)

机构地区：[1]六盘水师范学院数学与信息工程学院,贵州六盘水553004 [2]上饶师范学院数学与计算机科学学院,江西上饶334001

出　　处：《东北师大学报（自然科学版）》2020年第1期31-37,共7页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11571283);贵州省教育厅自然科学基金资助项目(KY[2019]139,KY[2019]143);六盘水师范学院校级项目(LPSSYKYJJ201801,LPSSYKJTD201907);上饶师范学院校级项目(201905).

摘　　要：研究了一类由小噪声驱动的具有时间依赖系数的非自治随机波动方程的渐近行为.在适当假设下证明了由该随机波动方程生成的非自治随机动力系统在空间H 10×L 2上存在唯一的拉回随机吸引子,并用正交投影的方法证明了系统在H 10×L 2上的拉回渐近紧性.This paper is concerned with the asymptotic behavior of a class of non-autonomous stochastic wave equation driven by small noise.It is shown that the non-autonomous dynamical system generated by the stochastic wave equation has a unique tempered pullback random attractor in the energy space H 10×L 2 when the density of the noise is suitable small and the time-dependent force is tempered,complement-small.The pullback asymptotic compactness of the system in H 10×L 2 is proved by using a canonical projection approach.

关 键 词：波动方程 非自治随机动力系统 拉回随机吸引子 小噪声 时间依赖的系统 

分 类 号：O193[理学—数学]