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 HAL: hal-00281709, version 1
 On the well-posedness for the coupling of multidimensional quasilinear diffusion-transport equations
 Gloria Aguilar 1, Laurent Levi ( ) 2
 (2008-05-23)
 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.
 1: Université de Saragosse Université de Saragosse 2: Laboratoire de Mathématiques et de leurs Applications de Pau (LMA-PAU) CNRS : UMR5142 – Université de Pau et des Pays de l'Adour [UPPA]
 Subject : Mathematics/Analysis of PDEs
 Keyword(s): Coupling problem – degenerate parabolic-hyperbolic equation – entropy solution
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 hal-00281709, version 1 http://hal.archives-ouvertes.fr/hal-00281709 oai:hal.archives-ouvertes.fr:hal-00281709 From: Laurent Lévi <> Submitted on: Monday, 26 May 2008 11:09:24 Updated on: Monday, 26 May 2008 13:40:21