二阶格点动力系统的随机一致指数吸引子  

Random Uniform Exponential Attractors for Second Order Lattice Dynamical Systems

作　　者：杨坚 周盛凡 Jian YANG;Sheng Fan(ZHOU School of Mathematical Sciences,Zhejiang Normal University,Jinhua 321004,P.R.China)

机构地区：[1]浙江师范大学数学科学学院,金华321004

出　　处：《数学学报（中文版）》2024年第1期21-44,共24页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11871437)。

摘　　要：本文主要考虑具有拟周期外力项和可乘白噪声的二阶格点系统在无穷序列加权空间中的随机一致指数吸引子的存在性.首先给出无穷序列加权空间的积空间上的联合连续随机动力系统的随机一致指数吸引子存在的充分条件.其次利用OrnsteinUhlenbeck过程,构造一个可逆变量代换将有白噪声的随机二阶格点系统(SDE)转化为无白噪声的随机二阶格点系统(RDE),证明RDE系统的解可以定义一个联合连续的随机动力系统.然后证明该联合连续随机动力系统的Lipschitz连续性,分解系统的两解之差为两个部分的和,并估计一些随机变量的期望.最后得到了所考虑系统的随机一致指数吸引子的存在性.We mainly consider the existence of random uniform exponential attractors in the weighted space of infinite sequences for second order lattice systems with quasi-periodic forces and multiplicative white noise.We first present some sufficient conditions for the existence of a random uniform exponential attractor for a jointly continuous random dynamical system defined on a product space of weighted space of infinite sequences.Secondly,by using Ornstein-Uhlenbeck process,a reversible variable substitution is constructed to transform the stochastic second-order lattice system(SDE)with white noise into a random system(RDE)without white noise,whose solutions generate a jointly continuous random dynamical system.Then we verify the Lipschitz continuity of the jointly continuous random dynamical system and decompose the difference between the two solutions of system into a sum of the two parts,and estimate the expectations of some random variables.Finally,we obtain the existence of random uniform exponential attractors for the considered system.

关 键 词：联合连续随机动力系统 二阶格点系统 随机一致指数吸引子 拟周期外力 可乘白噪声 

分 类 号：O193[理学—数学]