具有多个非线性源项的波动方程

刘亚成; 徐润章; 于涛

具有多个非线性源项的波动方程

哈尔滨工程大学理学院,哈尔滨 150001

基金项目: 国家自然科学基金资助项目(10271034)

详细信息

作者简介:
刘亚成(1941- ),男,吉林人,教授(Tel:+86-451-82518277);徐润章(1982- ),男,河北人,博士(联系人.E-mail:xurunzh@yahoo.com.cn).

中图分类号: O175.26；O175.27
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- 文章访问数: 3183
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- 被引次数: 0
出版历程
- 收稿日期: 2006-07-26
- 修回日期: 2007-06-28
- 刊出日期: 2007-09-15

Wave Equations With Several Nonlinear Source Terms

College of Science, Harbin Engineering University, Harbin 150001, P. R. China

摘要

摘要: 利用位势井方法研究在有界区域上具有多个非线性源项的波动方程初边值问题．给出了位势井的结构和位势井深度函数的性质．通过引进位势井族得到了在这些问题的流之下的一些集合不变性以及解的真空隔离，揭示了只要问题的初值属于位势井内或位势井外，则问题在今后所有时间内的解都存在于位势井内或井外，同时存在一个没有解的空间区域．进而给出了解的整体存在和不存在的门槛结果．最后,利用相同的方法讨论了具有临界初始条件的问题．
- 波动方程 /
- 位势井 /
- 整体存在性 /
- 不存在性
Abstract: The initial boundary value problem of nonlinear wave equations with several nonlinear source terms in a bounded domain is studied by potential well method. The structure of potential wells and some properties of depth function of potential well are given. The invariance of some sets under the flow of these problems and the vacuum isolating of solutions are obtained by introducing a family of potential wells, which indicates that if initial value of the problem belongs to potential well or its outside, all the solutions for the problem are in the same potential well or its outside respectively in any time. At the same time, there exists a region, in which there are no any solutions. Then the threshold result of global existence and nonexistence of solutions are given. Finally the problems with critical initial conditions are discussed.
- wave equation /
- potential well /
- global existence /
- nonexistence

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参考文献(15)

[1]	Sattinger D H.On global solution of nonlinear hyperbolic equations[J].Archive for Rational Mechanics and Analysis,1968,30:148-172.
[2]	Payne L E,Sattinger D H.Sadle points and instability of nonlinear hyperbolic equations[J]. Israel Journal of Mathematics,1975,22:273-303. doi: 10.1007/BF02761595
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[8]	Lions J L.Quelques Méthodes de Résolution des Problèmes aux Limites Nonlinéaires[M].Paris:Dunod Gauthier-Villars,1969.
[9]	Ikehata R.Some remarks on the wave equations with nonlinear damping and source terms[J].Nonlinear Analysis,1996,27(10):1165-1175. doi: 10.1016/0362-546X(95)00119-G
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[11]	Marcelo M,Cavalcanti,Valéria N.Domingos Cavalcanti,Existence and asymptotic stability for evolution problems on manifolds with damping and source terms[J].Journal of Mathematical Analysis and Applications,2004,291(1):109-127. doi: 10.1016/j.jmaa.2003.10.020
[12]	Marcelo M, Cavalcanti, Valéria N, Domingos Cavalcanti, Patrick Martinez.Existence and decay rate estimates for the wave equation with nonlinear boundary damping and source term[J].Journal of Differential Equations,2004,203(1):119-158. doi: 10.1016/j.jde.2004.04.011
[13]	Zhang J. On the standing wave in coupled non-linear Klein-Gordon equations[J].Mathematical Methods in the Applied Sciences,2003,26(1):11-25. doi: 10.1002/mma.340
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具有多个非线性源项的波动方程

作者简介:
刘亚成(1941- ),男,吉林人,教授(Tel:+86-451-82518277);徐润章(1982- ),男,河北人,博士(联系人.E-mail:xurunzh@yahoo.com.cn).

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Wave Equations With Several Nonlinear Source Terms

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留言板

具有多个非线性源项的波动方程

作者简介: 刘亚成(1941- ),男,吉林人,教授(Tel:+86-451-82518277);徐润章(1982- ),男,河北人,博士(联系人.E-mail:xurunzh@yahoo.com.cn).

计量

出版历程

Wave Equations With Several Nonlinear Source Terms

计量

出版历程

目录

作者简介:
刘亚成(1941- ),男,吉林人,教授(Tel:+86-451-82518277);徐润章(1982- ),男,河北人,博士(联系人.E-mail:xurunzh@yahoo.com.cn).