带调和势的随机非线性Schrdinger方程解的爆破(英文)  

Blow-up for the Stochastic Nonlinear Schrdinger Equation With a Harmonic Potential

作　　者：李姣[1,2] 张健[2] 

机构地区：[1]四川师范大学计算机软件省级重点实验室,成都四川610066 [2]四川师范大学数学与软件科学学院,成都四川610066

出　　处：《数学进展》2010年第4期491-499,共9页Advances in Mathematics（China）

基　　金：Supported by the NSFC(No.10747148,No.10771151);Scientific Research Fund of Sichuan Provincial Education Department(No.08ZA041)

摘　　要：本文讨论一类带调和势的随机非线性Schrdinger方程在临界或超临界情况下解的爆破性质.通过研究相关泛函的性质,证明了对任意带负能量的初值,解在概率意义下爆破.In this paper,we investigate the stochastic NLS（nonlinear Schrodinger） equation with a harmonic potential and then derive blow-up results in the critical and supercritical case.By studying the properties of related functionals,we prove that any given initial data with sufficient negative energy develops to a singularity in finite time with a positive probility.

关 键 词：随机非线性Schrdinger方程 加性噪声 调和势 负能量 爆破 

分 类 号：O175.27[理学—数学]