具有可乘白噪声和拟周期外力项的Boussinesq格点系统的随机一致指数吸引子  

Random Uniform Exponential Attractors for the Boussinesq Lattice System with Quasi-Periodic Forces and Multiplicative White Noise

作　　者：孙定杰 周盛凡 SUN DINGJIE;ZHOU SHENGFAN(College of Mathematics Sciences,Zhejiang Normal University,Jinhua 321004,China)

机构地区：[1]浙江师范大学数学科学学院,金华321004

出　　处：《应用数学学报》2025年第2期230-250,共21页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(批准号:11871437)资助项目。

摘　　要：主要考虑具有可乘白噪声和拟周期外力项的Boussinesq格点系统的随机一致指数吸引子的存在性.首先,利用Ornstein-Uhlenbeck过程将具有白噪声项的随机Boussinesq格点系统(SDE)转化为无白噪声项的随机Boussinesq格点系统(RDE).接着,证明RDE系统的解可定义联合连续的随机动力系统.然后,证明此系统存在一致吸收集并构造一个缓增有界闭的随机吸收集,验证系统在此吸收集上的Lipschitz连续性和随机挤压性,这可以通过估计解的“尾部”和对系统的两解之差做适当的分解来解决.最后,根据联合连续随机动力系统的随机一致指数吸引子存在的判据,得到本文所考虑的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 for the Boussinesq lattice system with quasi-periodic forces and multiplicative white noise.Firstly,by using the Ornstein-Uhlenbeck process,we transfer the stochastic Boussinesq lattice system(SDE) with multiplicative white noise into a random Boussinesq lattice system(RDE) without white noise.Then,we verify that this RDE system's solutions can define a jointly continuous random dynamical system.Next,we testify the existence of a uniform absorbing set for this system and construct a tempered bounded and closed absorbing random set.And we verify the Lipschitz continuity and the random squeezing property on this absorbing random set,which can be solved by estimating the "tail" of the solutions and decomposing the difference between two solutions of the system appropriately.Finally,according to the criterion for the existence of a random uniform exponential attractor for the jointly continuous random dynamical system,we obtain the existence of random uniform exponential attractors for the considered system of this paper.

关 键 词：可乘白噪声 拟周期 联合连续 随机动力系统 随机一致指数吸引子 

分 类 号：O193[理学—数学]