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 noi...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.展开更多
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)
文摘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.
