随机时滞复Ginzburg-Landau方程的遍历性  

Ergodicity for Stochastic Delay Complex Ginzburg-Landau Equations

作　　者：任蝶 邹艳艳 刘爱丽 舒级 REN Die;ZOU Yanyan;LIU Aili;SHU Ji(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,Sichuan;V.C.&V.R.Key Lab,Sichuan Normal University,Chengdu 610066,Sichuan)

机构地区：[1]四川师范大学数学科学学院,四川成都610066 [2]四川师范大学可视化计算与虚拟现实四川省重点实验室,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2025年第1期122-131,共10页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11371267和11571245);四川省科技厅应用基础计划项目(2016JY0204)。

摘　　要：讨论定义在整数集上的随机时滞复Ginzburg-Landau方程的遍历性.当非线性漂移项和扩散项是局部Lipschitz连续时,运用一致估计、二分法、Arzela-Ascoli定理建立有限维到无限维连续函数空间内解的概率分布的胎紧性,从而证明不变测度的存在性.当非线性飘移和扩散项的Lipschitz系数足够小时,证明不变测度的唯一性.In this paper,we discuss the ergodicity of the stochastic delay complex Ginzburg-Landau equations defined on the set of integers.When the nonlinear drift and diffusion terms are locally Lipschitz continous,we use the uniform tail-estimates,the technique of diadic division and the Arzela-Ascoli theorem to establish the tightness for probability distributions of solutions in the finite to infinite dimensional continuous function space which can prove the existence of the invariant measure.When the Lipschitz coefficients of the nonliner drift and diffusion terms are small enough,we prove the uniqueness of the invariant measure.

关 键 词：复GINZBURG-LANDAU方程 遍历性 不变测度 时滞 一致估计 

分 类 号：O175.29[理学—数学]