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一类带调和势的随机非线性Schrdinger方程的爆破解(英文) 被引量：2

Blow-up for the Stochastic Nonlinear Schrdinger Equation with Harmonic Potential
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摘要 讨论一类带调和势的随机非线性Schrdinger方程.众所周知,带白噪声的非线性Schrdinger方程描述了非线形色散波在非齐次或随机介质中的传播.首先给出带调和势的随机非线性Schrdinger方程的一些准备知识,通过建立该方程的性质,运用随机分析方法,证明了临界和超临界情形下解在对应能量空间中的爆破性质,推广了带调和势的非线性Schrdinger方程在确定情形下的相关结果. This paper discusses a class of stochastic nonlinear Schrodinger equations with harmonic potential. It is well known that the nonlinear Schrodinger equation with white noise describes the propagation of nonlinear dispersive waves in nonhomogeneous or random media. We first give some preliminaries of the stochastic nonlinear Schrodinger equation with harmonic potential. By establishing the properties of this equation and applying the arguments of stochastic analysis, we give blow-up of solutions in the critical and supercritical eases in corresponding energy space, which is the generalization of well-known results for nonlinear Sehrodinger equation in the deterministic case.
作者 舒级
机构地区 四川师范大学可视化计算与虚拟现实四川省重点实验室 四川师范大学数学与软件科学学院
出处 《四川师范大学学报（自然科学版）》 CAS CSCD 北大核心 2011年第6期906-910,共5页 Journal of Sichuan Normal University（Natural Science）
基金 supported by the National Natural Science Foundation of China(10926034,10747148) 四川省教育厅自然科学重点基金(11ZA101) 高等学校博士点基金(20105134110001)资助项目~~
关键词 随机非线性Schrdinger方程 调和势 乘性噪声 爆破解 stochastic nonlinear Schrodinger equation harmonic potential muhiplieative noise blow-up
分类号 O175.27 [理学—基础数学]
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参考文献20

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共引文献6

同被引文献26

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四川师范大学学报（自然科学版）
2011年 第6期

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