Distribution of resonances for the Neumann problem in linear elasticity outside a ball

P. Stefanov; G. Vodev

Annales de l'I.H.P. Physique théorique (1994)

  • Volume: 60, Issue: 3, page 303-321
  • ISSN: 0246-0211

How to cite

top

Stefanov, P., and Vodev, G.. "Distribution of resonances for the Neumann problem in linear elasticity outside a ball." Annales de l'I.H.P. Physique théorique 60.3 (1994): 303-321. <http://eudml.org/doc/76637>.

@article{Stefanov1994,
author = {Stefanov, P., Vodev, G.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {convergence; existence; cubic parabola},
language = {eng},
number = {3},
pages = {303-321},
publisher = {Gauthier-Villars},
title = {Distribution of resonances for the Neumann problem in linear elasticity outside a ball},
url = {http://eudml.org/doc/76637},
volume = {60},
year = {1994},
}

TY - JOUR
AU - Stefanov, P.
AU - Vodev, G.
TI - Distribution of resonances for the Neumann problem in linear elasticity outside a ball
JO - Annales de l'I.H.P. Physique théorique
PY - 1994
PB - Gauthier-Villars
VL - 60
IS - 3
SP - 303
EP - 321
LA - eng
KW - convergence; existence; cubic parabola
UR - http://eudml.org/doc/76637
ER -

References

top
  1. [A] J.D. Achenbach, Wave Propagation in Elastic Solid, North Holland, New York, 1973. Zbl0268.73005
  2. [BLR] C. Bardos, G. Lebeau and J. Rauch, Scattering Frequencies and Gevrey 3 Singularities, Invent. Math., Vol. 90, 1987, pp. 77-114. Zbl0723.35058MR906580
  3. [CP] F. Cardoso and G. Popov, Rayleigh Quasimodes in Linear Elasticity, Comm. P.D.E., Vol. 17, 1992, pp. 1327-1367. Zbl0795.35067MR1179289
  4. [Gr] R. Gregory, The Propagation of Rayleigh Waves over Curved Surfaces at High Frequency, Proc. Cambridge Philos. Soc., Vol. 70, 1971, pp. 103-121. Zbl0218.73036
  5. [G] J.C. Guillot, Existence and Uniqueness of a Rayleigh Surface Wave Propagating along the Free Boundary of a Transversely Isotropic Elastic Half Space, Math. Meth. Appl. Sci., Vol. 8, 1986, pp. 289-310. Zbl0606.73024MR845932
  6. [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., Vol. 6, 1989, pp. 83-95. Zbl0696.73017MR981515
  7. [IS] H. Iwashita and Y. Shibata, On the Analyticity of Spectral Function for Exterior Boundary Value Problems, Glas. Mat. Ser. III, 23, Vol. 43, 1988, pp. 291-313. Zbl0696.35120MR1012030
  8. [K] M. Kawashita, On the Local-Energy Decay Property for the Elastic Wave Equation with the Neumann Boundary Conditions, Duke Math. J., Vol. 67, 1992, pp. 333-351. Zbl0795.35061MR1177309
  9. [LP] P.D. Lax and R.S. Phillips, Scattering Theory, New York, Academic Press, 1967. Zbl0186.16301MR217440
  10. [MF] P. Morse and H. Feshbach, Methods of Theoretical Physics, McGrow-Hill, New York, 1953. Zbl0051.40603
  11. [O1] F. Olver, The Asymptotic Solution of Linear Differential Equations of Second Order for Large Values of a Parameter, Phylos. Trans. Royal Soc. London Ser. A., Vol. 247, pp. 307-327. Zbl0070.30801MR67249
  12. [02] F. Olver, The Asymptotic Expansion of Bessel Functions of Large Order, Phylos. Trans. Royal Soc. London Ser. A., Vol. 247, pp. 328-368. Zbl0070.30801MR67250
  13. [03] F. Olver, Asymptotics and Special Functions, Academic Press, New York, London, 1974. Zbl0303.41035MR435697
  14. [P] O. Poisson, Calculs des pôles de résonance associés à la diffraction d'ondes acoustiques et élastiques en dimension 2, thèse, Université Paris-IX. 
  15. [R] Lord Rayleigh, On Waves Propagated along Plane Surface of an Elastic Solid, Proc. London Math. Soc., Vol. 17, 1885, pp.4-11. Zbl17.0962.01JFM17.0962.01
  16. [RS] M. Reed and B. Simon, Methods of Modern Mathematical Physics II, Academic Press, New York, 1975. MR751959
  17. [SZ] J. Sjöstrand and M. Zworski, Complex scaling and the distribution of scattering poles, J. Amer. Math. Soc., Vol. 4, 4, 1991, pp. 729-769. Zbl0752.35046MR1115789
  18. [SS] Y. Shibata and H. Soga, Scattering Theory for the Elastic Wave Equation, Publ. R.I.M.S., Vol. 25, 1989, pp. 861-887. Zbl0714.35066MR1045996
  19. [T] 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, pp. 273-291. Zbl0432.73021MR535598
  20. [To] T. Tokita, Exponential Decay of Solutions for the Wave Equation in the Exterior Domain with Spherical Boundary, J. Math. Kyoto Univ., Vol. 12, 1972, pp. 413-430. Zbl0242.35049MR303096
  21. [V] B.R. Vainberg, Asymptotic Methods in Equations of Mathematical Physics, Gordon and Breach sci. publ., New York, 1988. Zbl0518.35002MR1054376

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.