Distribution des résonances pour le système de l'élasticité

G. Vodev; P. Stefanov

Séminaire Équations aux dérivées partielles (Polytechnique) (1993-1994)

  • page 1-8

How to cite

top

Vodev, G., and Stefanov, P.. "Distribution des résonances pour le système de l'élasticité." Séminaire Équations aux dérivées partielles (Polytechnique) (1993-1994): 1-8. <http://eudml.org/doc/112074>.

@article{Vodev1993-1994,
author = {Vodev, G., Stefanov, P.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {Neumann problem; eigenvalues; parametrix; exterior domains},
language = {fre},
pages = {1-8},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Distribution des résonances pour le système de l'élasticité},
url = {http://eudml.org/doc/112074},
year = {1993-1994},
}

TY - JOUR
AU - Vodev, G.
AU - Stefanov, P.
TI - Distribution des résonances pour le système de l'élasticité
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1993-1994
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 8
LA - fre
KW - Neumann problem; eigenvalues; parametrix; exterior domains
UR - http://eudml.org/doc/112074
ER -

References

top
  1. [A] J.D. Achenbach, Wave Propagation in Elastic Solid, North Holland, New York, 1973. Zbl0657.73019
  2. [BLR] C. Bardos, G. Lebeau And J. Rauch, Scattering frequencies and Gevrey 3 singularities, Invent. Math.90(1987), 77-114. Zbl0723.35058MR906580
  3. [CP] F. Cardoso AND G. Popov, Rayleigh quasimodes in linear elasticity, Comm. P.D.E.17(1992), 1327-1367. Zbl0795.35067MR1179289
  4. [D] J. Duistermaat, Oscillatory integrals, Lagrange immersions and unfolding of singularities, Comm. Pure Appl. Math.27(1974), 207-281. Zbl0285.35010MR405513
  5. [G] C. Gérard, Asymptotique des poles de la matrice de scattering pour deux obstacles strictement convex, Bull. Soc. Math. France, Mémoire n. 31, 116, 1988. Zbl0654.35081MR998698
  6. [Gr] R. Gregory, The propagation of Rayleigh waves over curved surfaces at high frequency, Proc. Cambridge Philos. Soc.70(1971), 103-121. Zbl0218.73036
  7. [Gu] J.C. Guillot, Existence and uniqueness of a Rayleigh surface wave propagating along the free bowndary of a transversely isotropic elastic half space, Math. Meth. Appl. Sci.8(1986), 289-310. Zbl0606.73024MR845932
  8. [HL] T. Hargé Et G. Lebeau, Diffraction par un convexe, preprint, Univ. Paris-Sud, 1993. 
  9. [I1] M. Ikawa, On the poles of the scattering matrix for two strictly convex obstacles, J. Math. Kyoto Univ.23-1(1983), 127-194. Zbl0561.35060MR692733
  10. [I2] M. Ikawa, Precise information on the poles of the scattering matrix for two strictly convex obstacles, J. Math. Kyoto Univ.27-1 (1987),69-102. Zbl0637.35068MR878491
  11. [I3] M. Ikawa, Trapping obstacles with a sequence of poles of the scattering matrix converging to the real axis, Osaka J. Math.22 (1985), 657-689. Zbl0617.35102MR815439
  12. [IN] M. Ikehata And G. Nakamura, Decaying and nondecaying properties of the local energy of an elastic wave outside an obstacle, Japan J. Appl. Math.6(1989), 83-95. Zbl0696.73017MR981515
  13. [K] M. Kawashita, On the local-energy decay property for the elastic wave equation with the Neumann boundary conditions, Duke Math. J.67(1992), 333-351. Zbl0795.35061MR1177309
  14. [LP1] P.D. Lax And R.S. Phillips, Scattering Theory, New York, Academic Press, 1967. Zbl0186.16301MR217440
  15. [LP2] P.D. Lax And R.S. Phillips, A logarithmic bound on the location of the poles of the scattering matrix, Arch. Rat. Mech. Anal.40 (1971), 268-280. Zbl0216.13002MR296534
  16. [M] R.B. Melrose, Polynomial bounds on the distribution of poles in scattering by an obstacle, Journées Équations aux dérivées partielles, Saint-Jean de Monts, 1984. Zbl0621.35073
  17. [M81] R.B. Melrose And J. Sjöstrand.Singularities of boundary value problems, I, Comm. Pure Appl. Math.31(1978), 593-617. Zbl0368.35020MR492794
  18. [MS2] R.B. Melrose And J. Sjöstrand, Singularities of boundary value problems, II, Comm. Pure Appl. Math.35(1982), 129-168 Zbl0546.35083MR644020
  19. [R] Lord Rayleigh, On waves propagated along plane surface of an elastic solid, Proc. London Math. Soc.17(1885), 4-11. Zbl17.0962.01JFM17.0962.01
  20. [S] M.A. Shubin, Pseudodifferential Operators and Spectral Theory, Springer, Berlin, Heidelberg, New York. 1987. Zbl0616.47040MR883081
  21. [SZ] J. Sjöstrand AND M. Zworski.The complex scaling method for scattering by strictly convex obstacles, preprint, Mittag-Leffler Inst., 1993. Zbl0839.35095MR1340273
  22. [SV1] P. Stefanov AND G. Vodev, Distribution of resonances for the Neumann problem in linear ellasticity outside a ball, Ann. Inst. II. Poincaré (Physique Théorique), to appear. Zbl0805.73016MR1281649
  23. [SV2] P. Stefanov AND G. Vodev, Distribution of resonances for the Neumann problem in linear ellasticity in the exterior of a strictly convex body, submitted. Zbl0846.35139
  24. [T1] M. Taylor, Rayleigh waves in linear elasticity as a propagation of singularities phenomenon, in Proc. Conf. on P.D.E. and Geometry, Marcel Dekker, New York, 1979, 273-291. Zbl0432.73021MR535598
  25. [T2] M. Taylor, Pseododifferential Operators, Princeton University Press, Princeton, 1981. Zbl0453.47026MR618463
  26. [Ti] E.C. Titchmarsh, The Theory of Functions, Oxford Univ. Press, Oxford, 1968. JFM65.0302.01
  27. [Y] K. Yamamoto, Singularities of solutions to the boundary value problems for elastic and Maxwell's equations, Japan J. Math.14(1988), 119-163. Zbl0669.73017MR945621
  28. [Va] B.R. Vainberg, Asymptotic Methods in Equations of Mathematical Physics, Gordon and Breach sci. publ., New York. 1988. Zbl0743.35001MR1054376
  29. [Vo] G. Vodev, Sharp bounds on the number of scattering poles for perturbations of the Laplacian, Comm. Math. Phys.146 (1992), 205-216. Zbl0766.35032MR1163673

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.