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

Gloria Aguilar (1) , Laurent Levi (2) , Monique Madaune-Tort (2)

1 Universidad de Zaragossa
2 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

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.

Mots clés: Coupling problem; degenerate parabolic-hyperbolic equation; entropy solution

Domaines: Equations aux dérivées partielles [math.AP]

Gloria Aguilar, Laurent Levi, Monique Madaune-Tort. On the well-posedness for the coupling of multidimensional quasilinear diffusion-transport equations. 2008. ⟨hal-00281709⟩