加权空间中随机部分耗散系统吸引子的存在性  

Attractors for random partly dissipative lattice dynamical systems in weight space

作　　者：张文兵[1] 黄瑞[1] 李全鹏[1] 

机构地区：[1]扬州大学数学科学学院,江苏扬州225002

出　　处：《扬州大学学报（自然科学版）》2009年第3期13-16,共4页Journal of Yangzhou University：Natural Science Edition

基　　金：江苏省自然科学基金资助项目(BK2007075);国家自然科学基金资助项目(60774073)

摘　　要：利用随机分析和泛函分析为工具研究加权空间中随机部分耗散系统的动力学行为.首先证明系统解的存在唯一性,并对这个解进行先验估计,通过论证得到系统吸收集的存在性;然后利用方程解的"尾部"在时间t足够大时任意小的性质讨论渐近紧性;最后证明系统全局吸引子的存在性.The dynamical behavior of the random partly dissipative lattice dynamical systems is discussed in this paper by using random analysis and functional analysis. The unique existence is first proved for the solutions of the random partly dissipative lattice dynamical systems, and a priori estimate is obtained on the solutions. The existence of an absorbing set is then discussed for the sys terns. An estimate on tails of the solutions is derived when the time is large enough, which ensures the asymptotic compactness of solutions. Finally, the global attractor is proved to exist.

关 键 词：随机 格子动力系统 全局吸引子 渐近紧性 

分 类 号：O193[理学—数学] O211.63[理学—基础数学]