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| HAL : hal-00262261, version 6 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (11-03-2008) | v2 (12-03-2008) | v3 (25-03-2008) | v4 (03-04-2008) | v5 (22-04-2008) | v6 (28-04-2008) |
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| Small Viscosity Solution of Linear Scalar Hyperbolic Problems with Discontinuous Coefficients in Several Space Dimensions. |
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| Bruno Fornet 1 |
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| (11/03/2008) |
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| In this paper we show that, for multi-D scalar nonconservative hyperbolic problems with an expansive discontinuity of the coefficient localized on $\{x_d=0\},$ a solution can successfully be singled out via a small viscosity approach. An interesting feature is that the so selected small viscosity solution is, in general, less regular than the data. Two stability results are also given under different assumptions on the coefficients. Finally, we give results about the small viscosity solution for discontinuous coefficients in either compressive setting or traversing setting. By doing so, we show that both the loss of regularity illustrated by Fig. 1. and the need to make a stability assumption on the coefficients are specific to discontinuous coefficients in expansive configuration. |
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| 1 : | Laboratoire d'Analyse, Topologie, Probabilités (LATP) |
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CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00262261, version 6 | |
| http://hal.archives-ouvertes.fr/hal-00262261 | |
| oai:hal.archives-ouvertes.fr:hal-00262261 | |
| Contributeur : Bruno Fornet | |
| Soumis le : Lundi 28 Avril 2008, 11:47:57 | |
| Dernière modification le : Lundi 28 Avril 2008, 11:50:11 | |
