Penalization approach to semi-linear symmetric hyperbolic problemswith dissipative boundary conditions

Bruno Fornet; O. Guès

doi:10.3934/dcds.2009.23.827

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2009, Volume 23, Issue 3: 827-845. Doi: 10.3934/dcds.2009.23.827

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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
2.
LATP, Univ. Aix-Marseille 1, 39 rue F. Joliot-Curie, 13453 Marseille cedex 13

Received: November 2007

Revised: May 2008

Published: September 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 35L50; Secondary: 65M99.

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