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

Gloria Aguilar Villa , Laurent Lévi

• This paper deals with the coupling of a quasilinear parabolic problem with a first order hyperbolic one in a multidimensional bounded domain n . In a region p a diffusion-advection-reaction type equation is set while in the complementary h ≡ \ p, only advection-reaction terms are taken into account. Suitable transmission conditions along the interface ∂ p ∩ ∂ 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.