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July  2009, 23(3): 827-845. doi: 10.3934/dcds.2009.23.827

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

Bruno Fornet 1, and  O. Guès 2,

1. 

LATP, Université de Provence, 39 rue Joliot-Curie, 13453 Marseille cedex 13, France
2. 

LATP, Univ. Aix-Marseille 1, 39 rue F. Joliot-Curie, 13453 Marseille cedex 13

Received  November 2007 Revised  May 2008 Published  November 2008

In this paper, we introduce a penalisation 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.
Keywords: Boundary layer, dissipative boundary conditions, characteristic boundary value problem, Domain penalization methods, non linear Hyperbolic problems.
Mathematics Subject Classification: Primary: 35L50; Secondary: 65M99.
Citation: Bruno Fornet, O. Guès. Penalization approach to semi-linear symmetric hyperbolic problems with dissipative boundary conditions. Discrete & Continuous Dynamical Systems, 2009, 23 (3) : 827-845. doi: 10.3934/dcds.2009.23.827
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