Équations aux dérivées partielles/Physique mathématique
Propagation des singularités et résonances
[Propagation of singularities and resonances]
Comptes Rendus. Mathématique, Volume 355 (2017) no. 8, pp. 887-891.

In the framework of semiclassical resonances, we make more precise the link between the polynomial estimates of the extension of the resolvent and the propagation of the singularities through the trapped set. This approach makes it possible to eliminate infinity and to concentrate the study near the trapped set. It has allowed us in previous papers to obtain the asymptotic of resonances in various geometric situations.

Dans le cadre de l'étude des résonances semiclassiques, on précise le lien entre majoration polynomiale du prolongement de la résolvante et propagation des singularités à travers l'ensemble capté. Cette approche permet d'éliminer l'infini et de concentrer l'étude près de l'ensemble capté. Nous l'avons utilisée dans des travaux antérieurs pour obtenir l'asymptotique des résonances dans diverses situations géométriques.

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Accepted:
Published online:
DOI: 10.1016/j.crma.2017.06.008
Bony, Jean-François 1; Fujiié, Setsuro 2; Ramond, Thierry 3; Zerzeri, Maher 4

1 IMB, CNRS (UMR 5251), université de Bordeaux, 33405 Talence, France
2 Department of Mathematical Sciences, Ritsumeikan University, 1-1-1 Noji-Higashi, Kusatsu, 525-8577 Japan
3 Laboratoire de mathématiques d'Orsay, université Paris-Sud, CNRS, université Paris-Saclay, 91405 Orsay, France
4 Université Paris-13, Sorbonne Paris Cité, LAGA, CNRS (UMR 7539), 93430 Villetaneuse, France
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Bony, Jean-François; Fujiié, Setsuro; Ramond, Thierry; Zerzeri, Maher. Propagation des singularités et résonances. Comptes Rendus. Mathématique, Volume 355 (2017) no. 8, pp. 887-891. doi : 10.1016/j.crma.2017.06.008. http://www.numdam.org/articles/10.1016/j.crma.2017.06.008/

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