无界域上Schrdinger型方程的整体吸引子

The Global Attractor for Schr■dinger Type Equation in an Unbounded Domain

本文证明了Schrodinger型方程u=（k＋iβ）Δu－|u|u-λu-g，u（x，0）=u0。其中u＝u（x，t），g=g（x），k＞0，ρ＞0，λ＞0，x∈Rn在加权Sobelev空间中强和弱吸引子的存在性，并对强吸引子的分形维数也给出了估计。

In this paper, we consider the initial value problem for schrodinger type equation tu= (k + iβ)Δu -|u|ρu - λu - g, u(x,0) = u0, where u = u(x,t),g =g(x),k >0,ρ>0,λ >0,x∈Rn. It is proved that the semigroup generated by this problem has a weak or/and strong grobal attractor in weighted sobolev space and its fractal dimension is finite.