Distribution of resonances for the Neumann problem in linear elasticity outside a ball
Annales de l'I.H.P. Physique théorique, Volume 60 (1994) no. 3, pp. 303-321.
@article{AIHPA_1994__60_3_303_0,
     author = {Stefanov, P. and Vodev, G.},
     title = {Distribution of resonances for the {Neumann} problem in linear elasticity outside a ball},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {303--321},
     publisher = {Gauthier-Villars},
     volume = {60},
     number = {3},
     year = {1994},
     mrnumber = {1281649},
     zbl = {0805.73016},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1994__60_3_303_0/}
}
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
SP  - 303
EP  - 321
VL  - 60
IS  - 3
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPA_1994__60_3_303_0/
LA  - en
ID  - AIHPA_1994__60_3_303_0
ER  - 
%0 Journal Article
%A Stefanov, P.
%A Vodev, G.
%T Distribution of resonances for the Neumann problem in linear elasticity outside a ball
%J Annales de l'I.H.P. Physique théorique
%D 1994
%P 303-321
%V 60
%N 3
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPA_1994__60_3_303_0/
%G en
%F AIHPA_1994__60_3_303_0
Stefanov, P.; Vodev, G. Distribution of resonances for the Neumann problem in linear elasticity outside a ball. Annales de l'I.H.P. Physique théorique, Volume 60 (1994) no. 3, pp. 303-321. http://www.numdam.org/item/AIHPA_1994__60_3_303_0/

[A] J.D. Achenbach, Wave Propagation in Elastic Solid, North Holland, New York, 1973.

[BLR] C. Bardos, G. Lebeau and J. Rauch, Scattering Frequencies and Gevrey 3 Singularities, Invent. Math., Vol. 90, 1987, pp. 77-114. | MR | Zbl

[CP] F. Cardoso and G. Popov, Rayleigh Quasimodes in Linear Elasticity, Comm. P.D.E., Vol. 17, 1992, pp. 1327-1367. | MR | Zbl

[Gr] R. Gregory, The Propagation of Rayleigh Waves over Curved Surfaces at High Frequency, Proc. Cambridge Philos. Soc., Vol. 70, 1971, pp. 103-121. | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[LP] P.D. Lax and R.S. Phillips, Scattering Theory, New York, Academic Press, 1967. | MR | Zbl

[MF] P. Morse and H. Feshbach, Methods of Theoretical Physics, McGrow-Hill, New York, 1953. | Zbl

[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. | MR | Zbl

[02] F. Olver, The Asymptotic Expansion of Bessel Functions of Large Order, Phylos. Trans. Royal Soc. London Ser. A., Vol. 247, pp. 328-368. | MR | Zbl

[03] F. Olver, Asymptotics and Special Functions, Academic Press, New York, London, 1974. | MR | Zbl

[P] O. Poisson, Calculs des pôles de résonance associés à la diffraction d'ondes acoustiques et élastiques en dimension 2, thèse, Université Paris-IX.

[R] Lord Rayleigh, On Waves Propagated along Plane Surface of an Elastic Solid, Proc. London Math. Soc., Vol. 17, 1885, pp.4-11. | JFM

[RS] M. Reed and B. Simon, Methods of Modern Mathematical Physics II, Academic Press, New York, 1975. | MR

[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. | MR | Zbl

[SS] Y. Shibata and H. Soga, Scattering Theory for the Elastic Wave Equation, Publ. R.I.M.S., Vol. 25, 1989, pp. 861-887. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[V] B.R. Vainberg, Asymptotic Methods in Equations of Mathematical Physics, Gordon and Breach sci. publ., New York, 1988. | MR