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.
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.
出处
《应用数学和力学》
CSCD
北大核心
2007年第9期1079-1086,共8页
Applied Mathematics and Mechanics
基金
国家自然科学基金资助项目(10271034)
关键词
波动方程
位势井
整体存在性
不存在性
wave equation
potential well
global existence
nonexistence
