数学物理学报 ›› 2011, Vol. 31 ›› Issue (6): 1461-1469.

• 论文 •    下一篇

关于剥脱现象的自由边值问题的研究

赵伟霞   

  1. 复旦大学数学科学学院 上海 200433
  • 收稿日期:2009-10-15 修回日期:2011-09-10 出版日期:2011-12-25 发布日期:2011-12-25
  • 基金资助:

    国家自然科学基金重点项目(11031001)和国家教育部博士点基金(20090071110002)资助.

Study on a Free Boundary Value Problem Arising from Peeling Phenomenon

 ZHAO Wei-Xia   

  1. School of Mathematical Science, Fudan University, Shanghai 200433
  • Received:2009-10-15 Revised:2011-09-10 Online:2011-12-25 Published:2011-12-25
  • Supported by:

    国家自然科学基金重点项目(11031001)和国家教育部博士点基金(20090071110002)资助.

摘要:

该文考虑一个产生于剥脱现象(Peeling Phenomenon)物理模型的自由边值问题
{utt-∂x(ux/√1+ux2)=0,    在{(t, x)|t>0, x>-l0}∩{u>0}中,

1/2ut2+1/√1+ux2-1+Q=0,   在{(t, x)|t>0, x>-l0}∩∂{u>0}上,
其中弦振动的非线性效应已被考虑. 这不同于K.Kikuchi, S.Omata等人曾研究的刻画Peeling Phenomenon 的自由边值问题. 作者在一些合理的假设下, 证明了此问题局部经典解的存在唯一性.

关键词: 剥脱现象, 自由边值问题, 非线性弦振动方程

Abstract:

In this paper the following free boundary problem
{utt-∂x(ux/√1+ux2)=0,    in{(t, x)|t>0, x>-l0}∩{u>0},

1/2ut2+1/√1+ux2-1+Q=0,   in{(t, x)|t>0, x>-l0}∩∂{u>0}
 is considered. The problem describes the peeling phenomenon. Different from the problem studied by K. Kikuchi and S. Omata,  the nonlinear effects in the vibrating string is also considered. Under some reasonable assumptions, the local existence and uniqueness of classical solution for the free boundary problem is proved.

Key words: Peeling phenomenon, Free boundary value problem, Nonlinear vibrating string equation

中图分类号: 

  • 35L70