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| HAL : hal-00565779, version 1 |
| arXiv : 1102.2873 |
| Fiche détaillée |  Récupérer au format |
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| A Gaussian beam approach for computing Wigner measures in convex domains |
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| Jean-Luc Akian 1Radjesvarane Alexandre 2 |
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| (14/02/2011) |
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| A Gaussian beam method is presented for the analysis of the energy of the high frequency solution to the mixed problem of the scalar wave equation in an open and convex subset, with initial conditions compactly supported in this set, and Dirichlet or Neumann type boundary condition. The transport of the microlocal energy density along the broken bicharacteristic flow at the high frequency limit is proved through the use of Wigner measures. Our approach consists first in computing explicitly the Wigner measures under an additional control of the initial data allowing to approach the solution by a superposition of first order Gaussian beams. The results are then generalized to standard initial conditions. |
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| 1 : | Aéroélasticité et dynamique des structures (ONERA - DADS) |
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ONERA |
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| 2 : | Institut de Recherche de l'Ecole Navale (EA 3634) (IRENAV) |
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Ecole Navale – Arts et Métiers ParisTech |
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| 3 : | Laboratoire de mécanique des sols, structures et matériaux (MSSMat) |
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CNRS : UMR8579 – Ecole Centrale Paris |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| wave equation – Gaussian beam summation – Wigner measures – FBI transform – reflection |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00565779, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00565779 | |
| oai:hal.archives-ouvertes.fr:hal-00565779 | |
| Contributeur : Radjesvarane Alexandre | |
| Soumis le : Lundi 14 Février 2011, 15:12:24 | |
| Dernière modification le : Lundi 14 Février 2011, 21:07:29 | |
