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一类带势的非线性Schrdinger方程对称爆破解的L^2集中性质 被引量：3

L^2-concentration of Symmetric Blow-up Solutions for Nonlinear Schrdinger Equations with Potential
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摘要 研究一类带势的非线性Schrdinger方程iut=-△u-k(t,x)|u|4/Nu,在二维空间中得到了其解在有限时间爆破的充分条件和其对称爆破解的L2集中性质. In this paper, a class of nonlinear Schrodinger equations with potential, iu,=-△u-k（t,x）｜u｜^4/Nu, is investigated in two-dimensional space. A sufficient condition for the solutions to blow-up in finite time is given, and L^2-concentration of blow-up solutions is proved.
作者 陈丹 张健 李晓光
机构地区 四川师范大学数学与软件科学学院 四川师范大学经济与管理学院
出处 《四川师范大学学报（自然科学版）》 CAS CSCD 北大核心 2008年第6期645-648,共4页 Journal of Sichuan Normal University（Natural Science）
基金 国家自然科学基金(10771151)资助项目
关键词 非线性SCHRODINGER方程 基态解 爆破解 爆破点 L^2集中 Nonlinear Schrodinger equation Ground state solution Blow-up solution Blow-up point L^2 -concentration
分类号 O175.24 [理学—基础数学]
  • 相关文献

参考文献18

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  • 9舒级,张健.一类带调和势的非线性Schrdinger方程[J].四川师范大学学报（自然科学版）,2002,25(2):129-131. 被引量：18
  • 10张健,舒级.低维空间中带调和势的非线性Schrdinger方程[J].四川师范大学学报（自然科学版）,2002,25(3):226-228. 被引量：13

二级参考文献44

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共引文献39

同被引文献28

  • 1郑斌.2+1维非线性Schrdinger方程的显式解[J].重庆师范大学学报（自然科学版）,2006,23(2):23-25. 被引量：7
  • 2周国中.叠加势V(r)=B_6■+B_5■+B_4■+B_3■+B_2■+B_1 r schrdinger方程的解析解[J].贵州师范大学学报（自然科学版）,2006,24(4):71-73. 被引量：3
  • 3Saito H,Ueda M.Intermittent implosion and pattern formation of trapped Bose-Einstein condensates with an attractive interaction[J].Phys Rev Lett,2001,86(4):1406-1409.
  • 4Oh Y G.Cauchy problem and Ehrenfest's law of nonlinear Schrodinger equations with potentials[J].J Differential Equations,1989,81(3):255-274.
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  • 6Fibich G.Self-focusing in the damped nonlinear Schrodinger equation[J].SIAM J Appl Math,2001,61(5):1680-1705.
  • 7Ohta M,Todorova G.Remarks on global existence and blowup for damped nonlinear Schrdinger equations[J].Discrete and Continuous Dynamical Systems,2009,23(6):1313-1325.
  • 8Zhang J.Stability of standing waves for nonlinear Schrodinger equations with unbounded potentials[J].Z Angew Math Phys,2000,51(5):498-503.
  • 9Bégout P.Necessary conditions and sufficient conditions for global existence in the nonlinear Schrdinger equation[J].Adv Math Sci Appl,2002,12(2):817-827.
  • 10Kono M, Skoric M, Ter Haar D. Spontaneous excitation of magnetic fields and collapse dynamics in a Langmuir plasma [ J ]. J Plasma Phvs, 1981:26 : 123 - 146.

引证文献3

二级引证文献6

四川师范大学学报（自然科学版）
2008年 第6期

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