一类非线性Schrdinger方程解的爆破  

Blow-up of Solutions for A Class of Nonlinear Schrdinger Equations

作　　者：王玲芝[1] 

机构地区：[1]涪陵师范学院数学系,重庆涪陵408003

出　　处：《渝州大学学报（自然科学版）》2002年第3期4-7,共4页Journal of Yuzhou University(Natural Sciences Edition)

摘　　要：研究了一类带调和势的非线性Schr dinger方程初值问题解的爆破性质。运用能量估计的方法 ,当初值u0 满足一定条件 ,并且设初值问题具有非正能量解时 ,可以得到存在一个有限时间T ,当时间t趋于T- 时 ,该初值问题的解u(t)的梯度在空间L2 (Rn)中趋于 +∞ ,亦即方程的解会在有限时间TThe blow_up of the initial value problem for a class of w onlinear Schrdinger equations with harmonic potential is studied. By using the method of energy estimate, When conditions satisfying the initial value uo are given and the equation with initial value problem is supposed to have solution w ith nonpositive energy, the following can be obtained:there exists a finite time T , as t tends to T - , the gradient of u(t) for the initial v alue problem tends to +∞ in space L 2(R n) , that is, the solutio n of equation will blow up in the finite time T<∞

关 键 词：解 爆破 非正能量解 非线性SCHROEDINGER方程 初值问题 能量估计 有限时间 

分 类 号：O175.29[理学—数学] O241.82[理学—基础数学]