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General anisotropic degenerate parabolic - hyperbolic equations homogeneous Dirichlet problem

Author: WuXuMing
Tutor: LiYaChun
School: Shanghai Jiaotong University
Course: Applied Mathematics
Keywords: Degenerate parabolic - hyperbolic equations Entropy Solutions Uniqueness Existence Bivariate methods Viscous elimination
CLC: O175.2
Type: Master's thesis
Year: 2012
Downloads: 9
Quote: 0
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Abstract


This paper studies the coefficient depends on the independent variable (t, x) in general anisotropic degenerate parabolic - hyperbolic equations with homogeneous Dirichlet Boundary Value Problems posedness . Degraded - parabolic hyperbolic equation with isotropic diffusion of research has been based. Anisotropic diffusion of , Chen-Perthame [1] in 2003 first proved by introducing a dynamic format Cauchy problem L1 dynamics Secretary existence and uniqueness of solutions . 2005 , Chen-Karlsen [2] on the coefficients depend on the independent variable while the general case , the establishment of the Cauchy problem for L ∞ existence and uniqueness of entropy solutions . While the initial boundary value problem , Li-Wang [3] first established the homogeneous Dirichlet problem for L ∞ existence and uniqueness of entropy solutions . On this basis , we study the independent variable coefficients depend on the general situation , the establishment of homogeneous Dirichlet problem L ∞ existence and uniqueness of entropy solutions . We introduce entropy - entropy flux triples and boundary entropy - entropy flow triples , given the definition of entropy solutions using Kruzkov bivariate entropy method proved the uniqueness of solution , using the elimination method proved sticky Entropy Solutions existence . Entropy Solutions uniqueness proved to be the focus of this article , which is on the border situation discussed in this paper to study the key points and difficult .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Partial Differential Equations
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