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| HAL : hal-00673138, version 1 |
| arXiv : 1202.5123 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (23-02-2012) | v2 (13-10-2012) |
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| Eigenmodes of the damped wave equation and small hyperbolic subsets |
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| Gabriel Riviere 1 |
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| (22/02/2012) |
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| We study high frequency stationary solutions of the damped wave equation on a compact and smooth Riemannian manifold without boundary. For a fixed damping parameter, we describe concentration properties of eigenmodes in neighborhoods of a fixed small hyperbolic subset with the same damping parameter. Precisely, we prove that, in the high frequency limit, a sequence of such modes cannot be completely localized in a shrinking tubes around such subsets. The article also includes an appendix (by S. Nonnenmacher and the author) where we establish the existence of an inverse logarithmic strip without eigenvalues below the real axis, under a pressure condition on the set of undamped trajectories. |
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| 1 : | Laboratoire de Mathématiques Paul Painlevé |
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CNRS : UMR8524 – Université Lille I - Sciences et technologies |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles Mathématiques/Théorie spectrale Mathématiques/Physique mathématique |
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| nonselfadjoint operators – semiclassical analysis – hyperbolic dynamical systems – eigenmodes – topological pressure |
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| hal-00673138, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00673138 | |
| oai:hal.archives-ouvertes.fr:hal-00673138 | |
| Contributeur : Gabriel Riviere | |
| Soumis le : Mercredi 22 Février 2012, 17:47:05 | |
| Dernière modification le : Jeudi 23 Février 2012, 10:15:55 | |
