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Problemes hyperboliques a coefficients discontinus et penalisation de problemes hyperboliques.

Abstract : This PhD Thesis is splitted into two parts.

1/ We are interested in the study of hyperbolic Cauchy problems with discontinuous coefficients.
We deal with discontinuities localized on one noncharacteristic hypersurface, also called interface, by using a vanishing viscosity approach. in different frameworks, we prove that the vanishing viscosity approach successfully singles out a unique solution. Different qualitative behaviors are shown to appear depending on the properties of the interface. in the case of systems, it is in general quite difficult to understand the properties of this interface.

2/ The goal here is to propose methods aimed at approximating the solutions of initial boundary value problems. More specifically, we propose domain penalization approaches for problems either well-posed in the sense of Friedrichs or well-posed in the sense of Kreiss.
The quality of the proposed methods are analyzed in terms of the boundary layers they generate.
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Contributor : Bruno Fornet <>
Submitted on : Friday, December 14, 2007 - 10:37:47 AM
Last modification on : Tuesday, February 5, 2019 - 11:44:10 AM
Long-term archiving on: : Monday, April 12, 2010 - 7:27:51 AM


  • HAL Id : tel-00197060, version 1



Bruno Fornet. Problemes hyperboliques a coefficients discontinus et penalisation de problemes hyperboliques.. Mathématiques [math]. Université de Provence - Aix-Marseille I, 2007. Français. ⟨tel-00197060⟩



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