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

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

Acta mathematica scientia,Series B ›› 2012, Vol. 32 ›› Issue (5): 1727-1742.doi: 10.1016/S0252-9602(12)60137-4

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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).

Abstract

Abstract:

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.

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

CLC Number:

35B40

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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References

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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

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