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| HAL : hal-00419335, version 1 |
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| Geometric optics expansions with amplification for hyperbolic boundary value problems: linear problems |
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| Jean-Francois Coulombel 1, 2Olivier Gues 3 |
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| (23/09/2009) |
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| We compute and justify rigorous geometric optics expansions for linear hyperbolic boundary value problems that do not satisfy the uniform Lopatinskii condition. We exhibit an amplification phenomenon for the reflection of small high frequency oscillations at the boundary. Our analysis has two important consequences for such hyperbolic boundary value problems. Firstly, we make precise the optimal energy estimate in Sobolev spaces showing that losses of derivatives must occur from the source terms to the solution. Secondly, we are able to derive a lower bound forthe finite speed of propagation, showing that waves may propagate faster than for the propagation in free space. We illustrate our analysis with some examples. |
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| 1 : | Laboratoire Paul Painlevé (LPP) |
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CNRS : UMR8524 – Université des Sciences et Technologies de Lille - Lille I |
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| 2 : | SIMPAF (INRIA Lille - Nord Europe) |
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INRIA – Université des Sciences et Technologies de Lille - Lille I – CNRS : UMR |
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| 3 : | 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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| Hyperbolic systems – boundary value problems – geometric optics |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00419335, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00419335 | |
| oai:hal.archives-ouvertes.fr:hal-00419335 | |
| Contributeur : Jean-Francois Coulombel | |
| Soumis le : Mercredi 23 Septembre 2009, 12:26:30 | |
| Dernière modification le : Mercredi 23 Septembre 2009, 13:35:22 | |
