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.