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

The aim of this paper is to prove the well-posedness（existence and uniqueness） of the L p entropy solution to the homogeneous Dirichlet problems for the anisotropic degenerate parabolic-hyperbolic equations with L p initial value.We use the device of doubling variables and some technical analysis to...

Full description

Saved in:
Bibliographic Details
Published in数学物理学报：B辑英文版 Vol. 32; no. 5; pp. 1727 - 1742
Main Author Wang Zhigang Li Yachun
Format Journal Article
LanguageEnglish
Published 01.09.2012
Subjects
Dirichlet问题
初值
双曲型方程
各向异性
拟线性
退化抛物型方程
退化抛物方程
齐次
Online AccessGet full text
ISSN0252-9602
1572-9087

Cover

More Information
Summary:The aim of this paper is to prove the well-posedness（existence and uniqueness） of the L p entropy solution to the homogeneous Dirichlet problems for the anisotropic degenerate parabolic-hyperbolic equations with L p initial value.We use the device of doubling variables and some technical analysis to prove the uniqueness result.Moreover we can prove that the L p entropy solution can be obtained as the limit of solutions of the corresponding regularized equations of nondegenerate parabolic type.
Bibliography:42-1227/O
Wang Zhigang , Li Yachun （1.Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China ; 2. Department of Mathematics, Fuyang Normal College, Fuyang 236029, China ）
degenerate parabolic-hyperbolic equation； L p entropy solution； device of doubling variables； vanishing viscosity method
The aim of this paper is to prove the well-posedness（existence and uniqueness） of the L p entropy solution to the homogeneous Dirichlet problems for the anisotropic degenerate parabolic-hyperbolic equations with L p initial value.We use the device of doubling variables and some technical analysis to prove the uniqueness result.Moreover we can prove that the L p entropy solution can be obtained as the limit of solutions of the corresponding regularized equations of nondegenerate parabolic type.
ISSN:0252-9602
1572-9087