| Publication type: |
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Preprint, Working Paper, ... |
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| Subject: |
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Mathematics/Analysis of PDEs
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| Title: |
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On the well-posedness for the coupling of multidimensional quasilinear diffusion-transport equations |
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| Author(s): |
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Gloria Aguilar ( ) 1, Laurent Levi ( ) 2, Monique Madaune-Tort () 2 |
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| Laboratory: |
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| Abstract: |
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This paper deals with the coupling of a quasilinear parabolic problem with a first order hyperbolic one in a multidimensional bounded domain $\Omega $. In a region $\Omega _{p}$ a diffusion-advection-reaction type equation is set while in the complementary $\Omega _{h}\equiv \Omega \backslash \Omega _{p}$, only advection-reaction terms are taken into account. Suitable transmission conditions along the interface $\partial \Omega _{p}\cap \partial \Omega _{h}$ are required. We select a weak solution characterized by an entropy inequality on the whole domain. This solution is given by a vanishing viscosity method. |
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| Fulltext language: |
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English |
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| Production date: |
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2008-05-23 |
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| Keyword(s): |
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Coupling problem – degenerate parabolic-hyperbolic equation – entropy solution |
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