华东师范大学学报(自然科学版) ›› 2009, Vol. 2009 ›› Issue (4): 78-81.

• 应用数学与基础数学 • 上一篇    下一篇

非线性边界条件下的线性波动方程的解

王丽华1、2   

  1. 1. 华东师范大学~~数学系, 上海 200062; 2. 苏州市职业大学~~基础部, 江苏~~苏州 215104
  • 收稿日期:2008-09-06 修回日期:2008-12-06 出版日期:2009-07-25 发布日期:2009-07-25
  • 通讯作者: 王丽华

Solutions to a linear wave equation with nonlinear\\[5pt] boundary conditions

WANG Li-hua1, 2   

  1. 1. {\it Department of Mathematics, East China Normal University, Shanghai} 200062, {\it China}

    2. {\it

    Department of Basic Courses, Suzhou Vocational University, Suzhou Jiangsu}215104, {\it China

  • Received:2008-09-06 Revised:2008-12-06 Online:2009-07-25 Published:2009-07-25
  • Contact: WANG Li-hua1

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摘要： 讨论一维线性波动方程和非线性边界条件的关系.
证明了一类一维线性波动方程在非线性边界条件下, 存在唯一的局部解.
同时也证明了由于边界条件的非线性, 初始值只要满足一定的条件, 即使很小,
对应的解也会在有限时间 内爆破. 在证明过程中, 同时给出了爆破时间的上界.

关键词: 波动方程, 局部存在性, 爆破, 波动方程, 局部存在性, 爆破

Abstract:

This paper was concerned with a one-dimensional linear wave equation
associated with nonlinear boundary conditions. The unique local solution to the wave
equation was proved to exist. The result is that the nonlinearity at the boundary causes
a finite time blow up of the solution, even for small initial data. And the upper bound
to the blow up time is given in the paper

Key words: local existence, blow up, wave equation, local existence, blow up

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