Impedance eigenvalues in linear elasticity
Abstract
This paper is devoted to studying impedance eigenvalues (that is, eigenvalues of a particular Dirichlet-to-Neumann map) for the time harmonic linear elastic wave problem, and their potential use as target-signatures for fluid-solid interaction problems. We first consider several possible families of eigenvalues of the elasticity problem, focusing on certain impedance eigenvalues that are an analogue of Steklov eigenvalues. We show that one of these families arises naturally in inverse scattering. We also analyse their approximation from far field measurements of the scattered pressure field in the fluid, and illustrate several alternative methods of approximation in the case of an isotropic elastic disk.
Cite
@article{arxiv.2103.14097,
title = {Impedance eigenvalues in linear elasticity},
author = {Michael Levitin and Peter Monk and Virginia Selgas},
journal= {arXiv preprint arXiv:2103.14097},
year = {2022}
}
Comments
This arXiv version corrects a misprint in formula (SM1.1) in the Supplementary materials in the published version. 24+6 pages, 5+2 figures, 0+1 tables