加权空间中带乘性噪声的随机分数阶非自治Ginzburg-Landau方程  

Stochastic Fractional Non-autonomous Ginzburg-Landau Equations with Multiplicative Noise in Weighted Space

作　　者：王云肖[1] 舒级[1] 杨袁[1] 李倩[1] 汪春江 WANG Yunxiao;SHU Ji;YANG Yuan;LI Qian;WANG Chunjiang(College of Mathematics Science,Sichuan Normal University,Chengdu 610066,Sichuan)

机构地区：[1]四川师范大学数学科学学院

出　　处：《四川师范大学学报（自然科学版）》2019年第4期491-500,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项目(2016JY0204)

摘　　要：考虑带乘性噪声的随机分数阶非自治Ginzburg-Landau方程在加权空间 Lρ^2( R^n )中的渐近性质.首先将随机偏微分方程转化为仅含随机参数的随机方程,然后对该方程的解进行先验估计,并通过尾估计得到渐近紧性成立,从而随机动力系统的紧性成立,最后证明 Lρ^2( R^n )中随机吸引子的存在性.In this paper, we consider the asymptotic dynamic for Random attractors of stochastic fractional non-autonomous Ginzburg-Landau equations with multiplicative noise in L 2 ρ( R n ). In the first, we transform the partial differential equation into the random equation that only indudes the random parameters. Then, using estimates for far-field values of solutions and a cut-off technique, asymptotic compactness is proved. At last, the existence of a random attractor in L 2 ρ( R n ) for the random dynamical system is established.

关 键 词：随机分数阶Ginzburg-Landau方程 随机动力系统 随机吸引子 乘性噪声 加权空间 

分 类 号：O175.2[理学—数学]