2006 International Conference in Honor of Jacqueline Fleckinger.
Electronic Journal of Differential Equations,
Conference 16 (2007), pp. 15-28. 

Title: Nonlinear multidimensional parabolic-hyperbolic equations

Authors: Gloria Aguilar (Univ. de Zaragoza, Spain)
         Laurent Levi   (Univ. de Pau, France)
	 Monique Madaune-Tort (Univ. de Pau, France)
 
Abstract: 
 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 at the interface
 $\partial\Omega_{p}\cap \partial\Omega_h$
 are required. We find a weak solution characterized by an entropy
 inequality on the whole domain.

Published May 15, 2007.
Math Subject Classifications: 35F25, 35K65.
Key Words: Coupling problem; degenerate parabolic-hyperbolic equation;
           entropy solution.