| 一类带调和势的随机非线性Schr(o)dinger方程的爆破解 |
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| 引用本文： | 舒级. 一类带调和势的随机非线性Schr(o)dinger方程的爆破解[J]. 四川师范大学学报(自然科学版), 2011, 34(6). DOI: 10.3969/j.issn.1001-8395.2011.06.027 |
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| 作者姓名： | 舒级 |
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| 作者单位： | 四川师范大学可视化计算与虚拟现实四川省重点实验室,四川成都610066;四川师范大学数学与软件科学学院,四川成都6100066 |
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| 基金项目： | the National Natural Science Foundation of China，四川省教育厅自然科学重点基金，高等学校博士点基金 |
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| 摘 要： | 讨论一类带调和势的随机非线性Schr(o)dinger方程.众所周知,带白噪声的非线性Schr(o)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(o)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(o)dinger方程在确定情形下的相关结果.
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| 关 键 词： | 随机非线性Schr(o)dinger方程 调和势 乘性噪声 爆破解 |
Blow-up for the Stochastic Nonlinear Schr(o)dinger Equation with Harmonic Potential |
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| SHU Ji. Blow-up for the Stochastic Nonlinear Schr(o)dinger Equation with Harmonic Potential[J]. Journal of Sichuan Normal University(Natural Science), 2011, 34(6). DOI: 10.3969/j.issn.1001-8395.2011.06.027 |
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| Authors: | SHU Ji |
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| Abstract: | This paper discusses a class of stochastic nonlinear Schr(o)inger equations with harmonic potential.It is well known that the nonlinear Schr(o)dinger 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 Schr(o)dinger 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 cases in corresponding energy space,which is the generalization of well-known results for nonlinear Schr(o)dinger equation in the deterministic case. |
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| Keywords: | ochastic nonlinear Schr(o)dinger equation harmonic potential multiplicative noise blow-up |
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