THE HOMOGENEOUS DIRICHLET PROBLEM FOR QUASILINEAR ANISOTROPIC DEGENERATE PARABOLIC-HYPERBOLIC EQUATION#br#
WITH Lp INITIAL VALUE

doi:10.1016/S0252-9602(12)60137-4

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (5): 1727-1742.doi: 10.1016/S0252-9602(12)60137-4

THE HOMOGENEOUS DIRICHLET PROBLEM FOR QUASILINEAR ANISOTROPIC DEGENERATE PARABOLIC-HYPERBOLIC EQUATION#br# WITH L^p INITIAL VALUE

王志刚^1,2|李亚纯^1*

1. Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China；
2. Department of Mathematics, Fuyang Normal College, Fuyang 236029, China

收稿日期:2011-09-19 出版日期:2012-09-20 发布日期:2012-09-20
通讯作者: 李亚纯，ycli@sjtu.edu.cn E-mail:wangzhigang@sjtu.edu.cn; ycli@sjtu.edu.cn
基金资助:
Yachun Li’s research was supported partly by National Natural Science Foundation of China (10571120, 10971135), the Program for New Century Excellent Talents of Chinese Ministry of Education (NCET-07-0546) and Shanghai Shuguang Project 06SG11. ZhigangWang’s research was supported partly by Shanghai Jiao Tong University Innovation Fund For Postgraduates (AE071202), the University Young
Teacher Sciences Foundation of Anhui Province (2010SQRL145) and the Quality Project Found of Fuyang Normal College (2010JPKC07).

THE HOMOGENEOUS DIRICHLET PROBLEM FOR QUASILINEAR ANISOTROPIC DEGENERATE PARABOLIC-HYPERBOLIC EQUATION#br# WITH L^p INITIAL VALUE

WANG Zhi-Gang^1,2, LI Ya-Chun^1*

1. Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China；
2. Department of Mathematics, Fuyang Normal College, Fuyang 236029, China

Received:2011-09-19 Online:2012-09-20 Published:2012-09-20
Contact: LI Ya-Chun，ycli@sjtu.edu.cn E-mail:wangzhigang@sjtu.edu.cn; ycli@sjtu.edu.cn
Supported by:
Yachun Li’s research was supported partly by National Natural Science Foundation of China (10571120, 10971135), the Program for New Century Excellent Talents of Chinese Ministry of Education (NCET-07-0546) and Shanghai Shuguang Project 06SG11. ZhigangWang’s research was supported partly by Shanghai Jiao Tong University Innovation Fund For Postgraduates (AE071202), the University Young
Teacher Sciences Foundation of Anhui Province (2010SQRL145) and the Quality Project Found of Fuyang Normal College (2010JPKC07).

摘要/Abstract

摘要：

The aim of this paper is to prove the well-posedness (existence and uniqueness) of the L^pentropy solution to the homogeneous Dirichlet problems for the anisotropic degenerate parabolic-hyperbolic equations with Lp initial value. We use the device of doubling variables and some technical analysis to prove the uniqueness result. Moreover we can prove that the Lp entropy solution can be obtained as the limit of solutions of the corresponding regularized equations of nondegenerate parabolic type.

关键词: degenerate parabolic-hyperbolic equation, L^p entropy solution, device of doubling variables, vanishing viscosity method

Abstract:

Key words: degenerate parabolic-hyperbolic equation, L^p entropy solution, device of doubling variables, vanishing viscosity method

中图分类号:

35B40

王志刚, 李亚纯. THE HOMOGENEOUS DIRICHLET PROBLEM FOR QUASILINEAR ANISOTROPIC DEGENERATE PARABOLIC-HYPERBOLIC EQUATION#br# WITH L^p INITIAL VALUE[J]. 数学物理学报(英文版), 2012, 32(5): 1727-1742.

WANG Zhi-Gang, LI Ya-Chun. THE HOMOGENEOUS DIRICHLET PROBLEM FOR QUASILINEAR ANISOTROPIC DEGENERATE PARABOLIC-HYPERBOLIC EQUATION#br# WITH L^p INITIAL VALUE[J]. Acta mathematica scientia,Series B, 2012, 32(5): 1727-1742.

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THE HOMOGENEOUS DIRICHLET PROBLEM FOR QUASILINEAR ANISOTROPIC DEGENERATE PARABOLIC-HYPERBOLIC EQUATION#br# WITH L^p INITIAL VALUE

THE HOMOGENEOUS DIRICHLET PROBLEM FOR QUASILINEAR ANISOTROPIC DEGENERATE PARABOLIC-HYPERBOLIC EQUATION#br# WITH L^p INITIAL VALUE

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THE HOMOGENEOUS DIRICHLET PROBLEM FOR QUASILINEAR ANISOTROPIC DEGENERATE PARABOLIC-HYPERBOLIC EQUATION#br# WITH Lp INITIAL VALUE

THE HOMOGENEOUS DIRICHLET PROBLEM FOR QUASILINEAR ANISOTROPIC DEGENERATE PARABOLIC-HYPERBOLIC EQUATION#br# WITH Lp INITIAL VALUE

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THE HOMOGENEOUS DIRICHLET PROBLEM FOR QUASILINEAR ANISOTROPIC DEGENERATE PARABOLIC-HYPERBOLIC EQUATION#br# WITH L^p INITIAL VALUE

THE HOMOGENEOUS DIRICHLET PROBLEM FOR QUASILINEAR ANISOTROPIC DEGENERATE PARABOLIC-HYPERBOLIC EQUATION#br# WITH L^p INITIAL VALUE