带调和势的非线性Schrdinger方程爆破解的爆破率  

Blow-up Rate of the Blow-up Solutions to Nonlinear Schrdinger Equations with Harmonic Potentials

作　　者：周展宏[1] 

机构地区：[1]广东海洋大学理学院,广东湛江524088

出　　处：《四川师范大学学报（自然科学版）》2007年第6期734-736,共3页Journal of Sichuan Normal University（Natural Science）

摘　　要：研究一类带调和势的非线性Schrdinger方程,根据带调和势与不带势的非线性Schrdinger方程之间的联系,以不带势的非线性Schrdinger方程的爆破率为基础,运用Carles(SIAM J.Math.Anal.,2003,35:823-843.)所建立的变换研究了带调和势的非线性Schrdinger方程爆破解,得到其爆破率的下界.We consider the Cauchy problem for a nonlinear Schrodinger equation with a harmonic potential. Caries （SIAM J. Math. Anal. ,2003,35：823-843. ） established the local existence and the existence of blow-up solutulons. Based on the relations between nonlinear Schrodinger equations with and without harmonic potential, we sdudy the blow-up solutions of nonlinear Schrodinger equation with a harmonic potential, using a tansformation established by Carles and the blow-up rate of the blow-up solution of nonlinear Schrodinger equation without harmonic potential, we establish the lower bound of the blow-up rate of the blow-up solutions for the nonlinear Schr＇odinger equation with a harmonic potential.

关 键 词：非线性Schrdinger方程 调和势 爆破率 

分 类 号：O175.28[理学—数学]