2006 International Conference in honor of Jacqueline Fleckinger. Electron. J. Diff. Eqns., Conference 16 (2007), pp. 15-28.

Nonlinear multidimensional parabolic-hyperbolic equations

Gloria Aguilar, Laurent Levi, Monique Madaune-Tort

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.

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Gloria Aguilar
Departamento de Matemática Aplicada
Universidad de Zaragoza, CPS
Maria de Luna 3, E-50018 Zaragoza, Spain
email: gaguilar@unizar.es
Laurent Lévi
Laboratoire de Mathématiques Appliquées, UMR 5142
Université de Pau, IPRA, BP 1155
F-64013 Pau Cedex, France
email: laurent.levi@univ-pau.fr
Monique Madaune-Tort
Laboratoire de Mathématiques Appliquées, UMR 5142
Université de Pau, IPRA, BP 1155
F-64013 Pau Cedex, France
email: monique.madaune-tort@univ-pau.fr

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