Fractal Dimension of Random Attractors for Non-autonomous Fractional Stochastic Ginzburg–Landau Equations

作     者：Chun Xiao GUO Ji SHU Xiao Hu WANG Chun Xiao GUO;Ji SHU;Xiao Hu WANG

作者机构：Department of MathematicsChina University of Mining and Technology BeijingBeijing 100083P.R.China School of Mathematical Science and V.C.&V.R.Key LabSichuan Normal UniversityChengdu 610068P.R.China Department of MathematicsSichuan UniversityChengdu 610064P.R.China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2020年第36卷第3期

页      面：318-336页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：Supported by National Natural Science Foundation of China(Grant Nos.11571245,11771444,11871138 and11871049) funding of V.C.&V.R.Key Lab of Sichuan Province the Yue Qi Young Scholar Project China University of Mining and Technology(Beijing) China Scholarship Council(CSC) 

主　　题：Non-autonomous stochastic fractional Ginzburg–Landau equation random dynamical system random attractor additive noise fractal dimension 

摘      要：This paper considers the dynamical behavior of solutions for non-autonomous stochastic fractional Ginzburg–Landau equations driven by additive noise with α∈(0, 1). First, we give some conditions for bounding the fractal dimension of a random invariant set of non-autonomous random dynamical system. Second, we derive uniform estimates of solutions and establish the existence and uniqueness of tempered pullback random attractors for the equation in H. At last, we prove the finiteness of fractal dimension of random attractors.