一类随机格点系统解的渐近行为  

Asymptotic Behavior of Solutions of a Stochastic Lattice Systems

作　　者：班爱玲 周恺 BAN AILING;ZHOU KAI(College of big data and artificial intelligence,Chizhou University,Chizhou 247000,China)

机构地区：[1]池州学院大数据与人工智能学院,池州247000

出　　处：《应用数学学报》2022年第6期821-837,共17页Acta Mathematicae Applicatae Sinica

基　　金：池州学院自然科学重点项目资助(CZ2020ZRZ07);安徽省课程思政教学团队(2020kcszjxtd57);安徽省一流本科专业建设点:数学与应用数学。

摘　　要：随机吸引子是描述随机动力系统状态的长时间渐近行为的一个主要工具,是目前动力系统研究的热点问题之一,讨论它的存在性具有十分重要意义.本文主要研究具有可乘白噪声的随机Klein-Gordon-Schrodinger(简称KGS)格点方程解的渐近行为.首先通过Ornstein-Uhlenbeck过程将具有可乘白噪声的KGS格点系统等价转换为不具有白噪声项的随机系统,证明其解的存在唯一性,其次论证该系统的解生成了一个连续随机动力系统,并存在一个缓增的随机有界吸收集,最后证明了该系统存在一个吸引所有缓增随机集的随机吸引子.Random attractor is a main tool to describe the long-time asymptotic behavior of the state of stochastic dynamic system.It is one of the hot issues in the research of dynamic system at present.It is of great significance to discuss its existence.This paper mainly studies the asymptotic behavior of the stochastic Klein-Gordon-Schrodinger(KGS)lattice equation with multiplicative white noise.Firstly,we equivalently transform the stochastic KGS lattice system into a random lattice system without noise term through the Ornstein-Uhlenbeck process,and prove the existence and uniqueness of solutions for the random lattice system.Then,it is proved that the solution of the system generates a continuous random dynamic system with a tempered random bounded absorbing set.Finally,we prove the existence of a random attractor which attracts all of the tempered random sets for the lattice system.

关 键 词：随机格点系统 Klein-Gordon-Schrodinger方程 可乘白噪声 随机吸引子 

分 类 号：O175[理学—数学]