[1]夏 滨.非相对论分子物理中带逆平方势的非线性Schrdinger方程的解整体存在[J].四川师范大学学报(自然科学版),2018,(05):648-653.[doi:10.3969/j.issn.1001-8395.2018.05.013]
 XIA Bin.Nonlinear Schrdinger Equation with Inverse Square Potential in Non-relativistic Molecular Physics[J].Journal of SichuanNormal University,2018,(05):648-653.[doi:10.3969/j.issn.1001-8395.2018.05.013]
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非相对论分子物理中带逆平方势的非线性Schrödinger方程的解整体存在()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2018年05期
页码:
648-653
栏目:
基础理论
出版日期:
2018-06-15

文章信息/Info

Title:
Nonlinear Schrödinger Equation with Inverse Square Potential in Non-relativistic Molecular Physics
文章编号:
1001-8395(2018)05-0648-06
作者:
夏 滨
四川建筑职业技术学院 教务处, 四川 德阳 618000
Author(s):
XIA Bin
Academic Affairs Office, Sichuan College of Architectural Technology, Deyang 618000, Sichuan
关键词:
非线性Schrödinger方程 逆平方势 整体存在
Keywords:
nonlinear Schrödinger equation inverse square potential global existence
分类号:
O175.29
DOI:
10.3969/j.issn.1001-8395.2018.05.013
文献标志码:
A
摘要:
在非相对论分子物理中带逆平方势的非线性Schrödinger方程模拟了有磁性的粒子捕获电子的现象.该系统的整体存在性被研究.对于次临界情形,证明了系统的解全部整体存在.对于临界情形,建立了系统解整体存在的一个L2标准.对于超临界情形,获得了系统解整体存在的一个H1标准.这些标准都是精确、显示和可计算的.
Abstract:
In non-relativistic molecular physics, nonlinear Schrödingerequation with inverse square potential can model the phenomenon of that a polar molecule captures one electron.It is very interesting to study the global existence of this system.For the subcritical case, the solution globally exists with any initial datum; for the critical case, an L2 initial datum criterion of the global existence is established; for the supercritical case, an H1 initial datum criterion of the global existence is derived.Moreover, these criteria are exact, explicit and computable.

参考文献/References:

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相似文献/References:

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 LI Jiao,ZHANG Jian.Global Solution for the Stochastic Nonlinear Schrödinger Equation with Critical Nonlinear Term[J].Journal of SichuanNormal University,2010,(05):143.
[2]夏滨.带逆平方势的非线性Schrdinger方程的阻尼影响[J].四川师范大学学报(自然科学版),2017,(06):802.[doi:10.3969/j.issn.1001-8395.2017.06.016]
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备注/Memo

备注/Memo:
收稿日期:2018-01-04 接受日期:2018-06-01
基金项目:四川省教育厅重点科研项目(15ZA0031)
作者简介:夏 滨(1969—),男,副教授,主要从事应用非线性分析的研究,E-mail:xiabin690215@163.com
更新日期/Last Update: 2018-04-15