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...
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| Published in | 数学物理学报：B辑英文版 Vol. 32; no. 5; pp. 1727 - 1742 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
01.09.2012
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0252-9602 1572-9087 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Wang Zhigang Li Yachun |
| AuthorAffiliation | Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China Department of Mathematics, Fuyang Normal Colleye, Fuyang 236029, China |
| Author_xml | – sequence: 1 fullname: Wang Zhigang Li Yachun |
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| Notes | 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. |
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| PublicationTitle | 数学物理学报：B辑英文版 |
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| PublicationYear | 2012 |
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| Snippet | 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... |
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| StartPage | 1727 |
| SubjectTerms | 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 |
| Title | THE HOMOGENEOUS DIRICHLET PROBLEM FOR QUASILINEAR ANISOTROPIC DEGENERATE PARABOLIC-HYPERBOLIC EQUATION WITH L~p INITIAL VALUE |
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