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On the well-posedness for the coupling of multidimensional quasilinear diffusion-transport equations

Gloria Aguilar 1, Laurent Levi (  Corresponding author ) 2, Monique Madaune-Tort 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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From: Laurent Lévi <>

Submitted on: Monday, 26 May 2008 11:09:24

Updated on: Monday, 26 May 2008 13:40:21