带有随机初值的复值Ginzburg-Landau方程的弱平均动力学  

Weak Mean Dynamics for Complex Ginzburg-Landau Equations with Random Initial Data

作　　者：陈章 李玲玉 CHEN Zhang;LI Lingyu(School of Mathematics,Shandong University,Jinan 250100,China)

机构地区：[1]山东大学数学学院,济南250100

出　　处：《数学年刊（A辑）》2022年第4期415-430,共16页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11471190,No.11971260)的资助。

摘　　要：本文研究了无界域上的带有随机初值的复值Ginzburg-Landau方程.首先,基于解过程的全局适定性,建立了带有随机初值的Ginzburg-Landau方程的平均随机动力系统.然后,证明了弱拉回平均随机吸引子的存在唯一性以及随机吸引子的周期性,并将其进一步推广到加权空间L2(Ω,Lσ2(R)).In this paper,complex-valued Ginzburg-Landau equations with random initial data on unbounded domains are investigated.First,based on the global well-posedness of solution processes,the mean random dynamical system associated with such equation with random initial data is established.Then,the existence and uniqueness of weak pullback mean random attractors are proved,as well as the periodicity of random attractors,which are further extended to a weighted space L~2(Ω,Lσ~2(R)).

关 键 词：复值Ginzburg-Landau方程 随机初值 平均随机动力系统 弱拉回平均吸引子 加权空间 

分 类 号：O175.29[理学—数学]