Mathematical Analysis for some Hyperbolic-Parabolic Coupled Problems

Julien Jimenez (1) , Laurent Levi (1)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

We deal with the mathematical analysis of the coupling problem in a bounded domain of $\R^n$, $n \geq 1$, between a purely quasilinear first-order hyperbolic equation set on a subdomain and a parabolic one, set on its complementary. We start by providing the definition of a weak solution through an entropy inequality on the whole domain. The uniqueness property relies on a pointwise inequality along the interface between the two subdomains and on the method of doubling variables. The existence proof is based on a vanishing viscosity method.

Domaines: Equations aux dérivées partielles [math.AP]

Julien Jimenez, Laurent Levi. Mathematical Analysis for some Hyperbolic-Parabolic Coupled Problems. 2009. ⟨hal-00418898⟩