数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (4): 1174-1188.doi: 10.1016/S0252-9602(10)60115-4

• 论文 • 上一篇    下一篇

INITIAL TRACE OF SOLUTIONS FOR A DOUBLY NONLINEAR DEGENERATE PARABOLIC EQUATIONS

王淑娟1, 2, 赵俊宁1   

  1. 1. School of Mathematics, Xiamen University, Xiamen 361005, China;

    2. Department of Information and Computation Science, Zhenzhou University of Light Industry, Henan 450002, China
  • 收稿日期:2007-12-27 修回日期:2008-09-18 出版日期:2010-07-20 发布日期:2010-07-20

INITIAL TRACE OF SOLUTIONS FOR A DOUBLY NONLINEAR DEGENERATE PARABOLIC EQUATIONS

 WANG Shu-Juan1, 2, ZHAO Jun-Ning1   

  1. 1. School of Mathematics, Xiamen University, Xiamen 361005, China;

    2. Department of Information and Computation Science, Zhenzhou University of Light Industry, Henan 450002, China
  • Received:2007-12-27 Revised:2008-09-18 Online:2010-07-20 Published:2010-07-20

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摘要：

In this note, we study the existence of an initial trace of nonnegative solutions for the following problem
ut-div(|\bigtriangledown um|p-2\bigtriangledownum)+uq=0  in  QT=Ω×(0, T).
We prove that the initial trace is an outer regular Borel measure, which may not be locally bounded for some values of parameters p, q, and m. We also  study  the corresponding Cauchy problems with a given generalized Borel measure as initial data.

关键词: Doubly degenerate, Initial trace, Borel measure

Abstract:

In this note, we study the existence of an initial trace of nonnegative solutions for the following problem
ut-div(|\bigtriangledown um|p-2\bigtriangledownum)+uq=0  in  QT=Ω×(0, T).
We prove that the initial trace is an outer regular Borel measure, which may not be locally bounded for some values of parameters p, q, and m. We also  study  the corresponding Cauchy problems with a given generalized Borel measure as initial data.

Key words: Doubly degenerate, Initial trace, Borel measure

中图分类号: 

  • 35K20
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