非自治Schr dinger方程的近似惯性流形

Approximate Inertial Manifolds for the Non-autonomous Schrdinger Equations

研究具有耗散性质的非自治Schr dinger方程ut-(λ+iα)Δu +( k +iβ) | u|2u -γu =f(t ,x) ,运用具有两个参数的算子簇———“过程”来描述此无穷维动力系统,构建了其近似惯性流形,进一步获得此近似惯性流形逼近方程一致吸引子的阶数的近似估计.

In this paper, the dissipative non-autonomous Schroedinger equation δu/δt-（λ＋iα）Δu＋（k＋iβ）｜u｜^2-γu=f（t,x） is studied. Applying the process which describes the infinite dynamical system using the operator family of two parameters, the approximate inertial manlfolds（AIM） is constructed. Furthermore, the estimate of the order to the AIM which approachs the global attractor has been obtained.