ASYMPTOTIC BEHAVIOR FOR GENERALIZED GINZBURG-LANDAU POPULATION EQUATION WITH STOCHASTIC PERTURBATION  

作　　者：Jiahe Xu Kang Zhou Qiuying Lu 

机构地区：[1]Dept.of Math.,Zhejiang Sci-Tech University

出　　处：《Annals of Applied Mathematics》2016年第2期174-182,共9页应用数学年刊（英文版）

基　　金：the grant of China Scholarship Council,National Natural Science Foundation of P.R.China(No.11101370,No.11302150,No.11211130093);the "521" talent program of Zhejiang Sci-Tech University(No.11430132521304);Zhejiang Provincial Natural Science Foundation(LY13A010014)

摘　　要：In this paper,we are devoted to the asymptotic behavior for a nonlinear parabolic type equation of higher order with additive white noise.We focus on the Ginzburg-Landau population equation perturbed with additive noise.Firstly,we show that the stochastic Ginzburg-Landau equation with additive noise can be recast as a random dynamical system.And then,it is proved that under some growth conditions on the nonlinear term,this stochastic equation has a compact random attractor,which has a finite Hausdorff dimension.In this paper,we are devoted to the asymptotic behavior for a nonlinear parabolic type equation of higher order with additive white noise.We focus on the Ginzburg-Landau population equation perturbed with additive noise.Firstly,we show that the stochastic Ginzburg-Landau equation with additive noise can be recast as a random dynamical system.And then,it is proved that under some growth conditions on the nonlinear term,this stochastic equation has a compact random attractor,which has a finite Hausdorff dimension.

关 键 词：Ginzburg-Landau model additive white noise random attractor Hausdorff dimension 

分 类 号：O175[理学—数学]