INITIAL TRACE OF SOLUTIONS FOR A DOUBLY NONLINEAR DEGENERATE PARABOLIC EQUATIONS

doi:10.1016/S0252-9602(10)60115-4

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

INITIAL TRACE OF SOLUTIONS FOR A DOUBLY NONLINEAR DEGENERATE PARABOLIC EQUATIONS

王淑娟^{1, 2}, 赵俊宁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-Juan^{1, 2}, ZHAO Jun-Ning¹

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

摘要/Abstract

摘要：

In this note, we study the existence of an initial trace of nonnegative solutions for the following problem
u_t-div(|\bigtriangledown u^m|^p-2\bigtriangledownu^m)+u^q=0 in Q_T=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:

Key words: Doubly degenerate, Initial trace, Borel measure

中图分类号:

35K20

王淑娟, 赵俊宁. INITIAL TRACE OF SOLUTIONS FOR A DOUBLY NONLINEAR DEGENERATE PARABOLIC EQUATIONS[J]. 数学物理学报(英文版), 2010, 30(4): 1174-1188.

WANG Shu-Juan, ZHAO Jun-Ning. INITIAL TRACE OF SOLUTIONS FOR A DOUBLY NONLINEAR DEGENERATE PARABOLIC EQUATIONS[J]. Acta mathematica scientia,Series B, 2010, 30(4): 1174-1188.

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INITIAL TRACE OF SOLUTIONS FOR A DOUBLY NONLINEAR DEGENERATE PARABOLIC EQUATIONS

INITIAL TRACE OF SOLUTIONS FOR A DOUBLY NONLINEAR DEGENERATE PARABOLIC EQUATIONS

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