Lower bound for the number of the Rayleigh resonances for arbitrary body. (English) Zbl 0961.35098

Stefanov, Plamen

Indiana Univ. Math. J. 49, No. 1, 405-426 (2000).

This paper discusses the system of linear elasticity in an exterior domain in \(\mathbb{R}^3\) with Neumann boundary conditions. The author proves an optimal bound for the asymptotic distribution of the resonances near the real axis due to the existence of Rayleigh waves. The author constructs real quasimodes as the eigenvalues of an elliptic first-order \(\Psi DO \) on the boundary. In case of a convex boundary, the author proves that the resonance states are asymptotically close to the quasimode states and uses this to find explicitly the leading term of the resonance states on the boundary.

Reviewer: Zhang Wanguo (Shanghai)

MSC:

35P25	Scattering theory for PDEs
78A40	Waves and radiation in optics and electromagnetic theory
35J55	Systems of elliptic equations, boundary value problems (MSC2000)
35S99	Pseudodifferential operators and other generalizations of partial differential operators

Keywords:

linear elasticity system; Neumann problem; Rayleigh resonances