Resumen de Analysis of a coupled parabolic-hyperbolic problem

Laurent Lévi, Monique Madaune-Tort , Gloria Aguilar Villa

• This paper deals with the mathematical analysis of a quasilinear parabolichyperbolic problem in a multidimensional bounded domain W. In a region Wp a diffusionadvection- reaction type equation is set while in the complementary Wh  W\Wp, only advection-reaction terms are taken into account. To begin we provide the definition of a weak solution through an entropy inequality on the whole domain. Since the interface ¶Wp\¶Wh contains outward characteristics for the first-order operator in Wh, the uniqueness proof starts by considering first the hyperbolic zone and then the parabolic one. The existence property uses the vanishing viscosity method and to pass to the limit on the hyperbolic zone, we refer to the notion of process solution