数学物理学报 ›› 2013, Vol. 33 ›› Issue (6): 1001-1012.

• 论文 •    下一篇

剥脱现象中的某个自由边值问题的整体经典解

赵伟霞   

  1. 复旦大学数学科学学院 上海 200433
  • 收稿日期:2012-01-10 修回日期:2013-02-27 出版日期:2013-12-25 发布日期:2013-12-25
  • 作者简介:国家自然科学基金重点项目“非线性双曲型与混合型偏微分方程”(11031001)和教育部博士点基金“跨音速流与非线性混合型方程”(20090071110002)资助
  • 基金资助:

    国家自然科学基金重点项目“非线性双曲型与混合型偏微分方程"(11031001)和教育部博士点基金”跨音速流与非线性混合型方程"(20090071110002)资助

The Global Classical Solution to a Free Boundary Problem in the Peeling Phenomenon

 ZHAO Wei-Xia   

  1. School of Mathematical Science, Fudan University, Shanghai 200433
  • Received:2012-01-10 Revised:2013-02-27 Online:2013-12-25 Published:2013-12-25
  • Supported by:

    国家自然科学基金重点项目“非线性双曲型与混合型偏微分方程”(11031001)和教育部博士点基金“跨音速流与非线性混合型方程”(20090071110002)资助

摘要:

考虑一个不带初始区间的自由边值问题, 该问题产生于剥脱现象(Peeling Phenomenon)的物理模型. 在一些物理模型中自然成立的条件下, 证明了此问题局部经典解的存在唯一性. 在两类有交集但不重合的假设条件下, 证明了此问题整体经典解的存在唯一性.

关键词: 剥脱现象, 自由边值问题, 整体解的存在唯一性

Abstract:

In the paper, a free boundary problem which arises in the peeling phenomenon without an initial interval is considered. The local existence and uniqueness of the classical solution to the problem  are obtained under some conditions which
are naturally satisfied in the physical model. The global existence and uniqueness of the classical solution are also obtained under two kinds of assumptions which intersect but do not contain each other.

Key words: Free boundary problem, Peeling phenomenon, Global existence and uniqueness

中图分类号: 

  • 35L70