Résonances de Rayleigh en dimension deux

Didier Gamblin[1]

  • [1] LAGA, Institut Galilée, Université Paris 13

Séminaire Équations aux dérivées partielles (2003-2004)

  • Volume: 2003-2004, page 1-10

How to cite

top

Gamblin, Didier. "Résonances de Rayleigh en dimension deux." Séminaire Équations aux dérivées partielles 2003-2004 (2003-2004): 1-10. <http://eudml.org/doc/11095>.

@article{Gamblin2003-2004,
affiliation = {LAGA, Institut Galilée, Université Paris 13},
author = {Gamblin, Didier},
journal = {Séminaire Équations aux dérivées partielles},
language = {fre},
pages = {1-10},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Résonances de Rayleigh en dimension deux},
url = {http://eudml.org/doc/11095},
volume = {2003-2004},
year = {2003-2004},
}

TY - JOUR
AU - Gamblin, Didier
TI - Résonances de Rayleigh en dimension deux
JO - Séminaire Équations aux dérivées partielles
PY - 2003-2004
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2003-2004
SP - 1
EP - 10
LA - fre
UR - http://eudml.org/doc/11095
ER -

References

top
  1. M.Bellassoued, Distributions of resonances and decay rate of the local energy for the elastic wave equation. Comm.Math.Phys.,vol.215, 2000, p.375-408. Zbl0978.35077MR1799852
  2. N.Burq, Décroissance de l’énergie locale de l’équation des ondes pour le problème extérieur et absence de résonance au voisinage du réel. Acta Math. 180, 1998, n 1, pp.1-29. Zbl0918.35081
  3. D.Gamblin, Résonances de Rayleigh en dimension deux. Thèse de doctorat de l’Univ. Paris 13, 2002. 
  4. D.Gamblin, Résonances de Rayleigh en dimension deux. A paraître au Bulletin de la SMF. Zbl1134.35384
  5. D.Gamblin, Partie imaginaire des résonances de Rayleigh dans le cas d’une boule. En préparation. Zbl05042532
  6. A.Grigis, J.Sjöstrand, Microlocal analysis for differential operators. London Mathematical Society, Lecture note series 196. Zbl0804.35001MR1269107
  7. B.Helffer, J.Sjöstrand, Résonances en limite semi-classique. Mémoire de la S.M.F.(N.S.), n 24-25, 1986. Zbl0631.35075MR871788
  8. B.Helffer, J.Sjöstrand, Analyse semi-classique pour l’équation de Harper II. Mémoire de la S.M.F., 40, 1990. Zbl0714.34131
  9. M.Ikehata, G.Nakamura, Decaying and nondecaying properties of the local energy of an elastic wave outside an obstacle. Japan Journal Appl. Math., vol 6, 1989, p.83-95. Zbl0696.73017MR981515
  10. M.Kawashita, On the local-energy decay property for the elastic wave equation with the Neumann boundary conditions. Duke Mathematical Journal, vol.67, 1992, p.333-351. Zbl0795.35061MR1177309
  11. J.Sjöstrand, G.Vodev, Asymptotics of the number of Rayleigh resonances. Matematische Annalen, 309, p.287-306, 1997. Zbl0890.35098MR1474193
  12. J.Sjöstrand, Singularités analytiques microlocales. Astérisque vol. 95, 1982. Zbl0524.35007MR699623
  13. J.Sjöstrand, M.Zworski, Complex scaling method and the distribution of scattering poles. Journal of the American Mathematical Society, vol.4, 1991, p.729-769. Zbl0752.35046MR1115789
  14. P.Stefanov, Quasimodes and resonances : Sharp lower bounds. Duke Mathematical Journal, vol.99, n 1, 1999, p.75-92. Zbl0952.47013MR1700740
  15. P.Stefanov, Lower bound of the number of the Rayleigh resonances for arbitrary body. Indiana University Math. Journal, vol.49, n 1, 2000, p.405-426. Zbl0961.35098MR1777025
  16. P.Stefanov, Resonance expansions and Rayleigh waves. Math.Res.Lett.8 (1-2) (2001), p.105-124. Zbl0987.35097MR1825264
  17. P.Stefanov, G.Vodev, Distribution of resonances for the Neumann problem in linear elasticity outside a ball. Annales de l’Institut H.Poincaré (Physique théorique), vol. 60, n 3, 1994, p.303-321. Zbl0805.73016
  18. P.Stefanov, G.Vodev, Distribution of resonances for the Neumann problem in linear elasticity in the exterior of a strictly convex body. Duke Mathematical Journal, vol. 78, n 3 , 1995, p.677-714. Zbl0846.35139MR1334206
  19. P.Stefanov, G.Vodev, Neumann resonances in linear elasticity for an arbitrary body. Comm. Math. Phys., vol.176, 1996, p.645-659. Zbl0851.35032MR1376435
  20. S.-H.Tang, M.Zworski, Resonances expansions of scattered waves. Comm. Pure Appl. Math. 53 (2000), p.1305-1334. Zbl1032.35148MR1768812
  21. M.Taylor, Rayleigh waves in linear elasticity as a propagation of singularities phenomenon, in proceedings of the Conference on Partial Differential Equations and Geometry, Marcel Dekker, New York, 1979, p.273-291. Zbl0432.73021MR535598
  22. G.Vodev, Existence of Rayleigh resonances exponentially close to the real axis. Annales de l’Institut H.Poincaré (Physique théorique), vol.67, n 1 , 1997, p.41-57. Zbl0893.35088

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.