Existence of Rayleigh resonances exponentially close to the real axis
Annales de l'I.H.P. Physique théorique, Volume 67 (1997) no. 1, p. 41-57
@article{AIHPA_1997__67_1_41_0,
author = {Vodev, G.},
title = {Existence of Rayleigh resonances exponentially close to the real axis},
journal = {Annales de l'I.H.P. Physique th\'eorique},
publisher = {Gauthier-Villars},
volume = {67},
number = {1},
year = {1997},
pages = {41-57},
zbl = {0893.35088},
mrnumber = {1463004},
language = {en},
url = {http://www.numdam.org/item/AIHPA_1997__67_1_41_0}
}

Vodev, G. Existence of Rayleigh resonances exponentially close to the real axis. Annales de l'I.H.P. Physique théorique, Volume 67 (1997) no. 1, pp. 41-57. http://www.numdam.org/item/AIHPA_1997__67_1_41_0/

[1] 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 1177309 | Zbl 0795.35061

[2] M. Kawashita, On a region free from the poles of the resolvent and decay rate of the local energy for the elastic wave equation, Indiana Univ. Math. J., Vol. 43, 1994, pp. 1013-1043. | MR 1305958 | Zbl 0832.35088

[3] J. Sjöstrand, Singularités analytiques microlocales, Astérisque, Vol. 95, 1982. | MR 699623 | Zbl 0524.35007

[4] J. Sjöstrand and G. Vodev, Asymptotics of the number of Rayleigh resonances, Math. Ann., to appear. | MR 1474193 | Zbl 0890.35098

[5] P. Stefanov and G. Vodev, Distribution of resonances for the Neumann problem in linear elasticity outside a ball, Ann. Inst. H.Poincaré (Physique Théorique), Vol. 60, 1994, pp. 303-321. | Numdam | MR 1281649 | Zbl 0805.73016

[6] P. Stefanov and G. Vodev, Distribution of resonances for the Neumann problem in linear elasticity outside a strictly convex body, Duke Math. J., Vol. 78, 1995, pp. 677-714. | MR 1334206 | Zbl 0846.35139

[7] P. Stefanov and G. Vodev, Neumann resonances in linear elasticity for an arbitrary body, Commun. Math. Phys., Vol. 176, 1996, pp. 645-659. | MR 1376435 | Zbl 0851.35032

[8] 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 535598 | Zbl 0432.73021

[9] G. Vodev, Sharp bounds on the number of scattering poles for perturbations of the Laplacian, Commun. Math. Phys., Vol. 146, 1992, pp. 205-216. | MR 1163673 | Zbl 0766.35032

[10] H. Walker, Some remarks on the local energy decay of solutions of the initial-boundary value problem for the wave equation in unbounded domains, J. Diff. Equations, Vol. 23, 1977, pp. 459-471. | MR 427797 | Zbl 0337.35046

[11] K. Yamamoto, Singularities of solutions to the boundary value problems for elastic and Maxwell's equations, Japan J. Math., Vol. 14, 1988, pp. 119-163. | MR 945621 | Zbl 0669.73017