Penalization approach of semi-linear symmetric hyperbolic problems with dissipative boundary conditions

Bruno Fornet (1, 2) , Olivier Guès (1)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 LMRS - Laboratoire de Mathématiques Raphaël Salem

In this paper, we introduce a penalization method in order to approximate the solutions of the initial boundary value problem for a semi-linear first order symmetric hyperbolic system, with dissipative boundary conditions. The penalization is carefully chosen in order that the convergence to the wished solution is sharp, does not generate any boundary layer, and applies to fictitious domains.

Domaines: Equations aux dérivées partielles [math.AP]

Bruno Fornet, Olivier Guès. Penalization approach of semi-linear symmetric hyperbolic problems with dissipative boundary conditions. 2007. ⟨hal-00160777v2⟩