About embedded eigenvalues for a spectral problem arising in the study of elastic surface waves in a topographical waveguide
✍ Scribed by Mourad Sini
- Publisher
- John Wiley and Sons
- Year
- 2002
- Tongue
- English
- Weight
- 161 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0170-4214
- DOI
- 10.1002/mma.324
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✦ Synopsis
Abstract
In this paper, we are interested with the spectral study of an operator given by an elastic topographical waveguide, a deformed half‐space, of which the cross‐section is a local perturbation of a homogeneous half‐plane. We look for guided waves propagating more rapidly than Rayleigh waves (which mathematically would correspond to embedded eigenvalues) and prove that there are no guided waves propagating more rapidly than S‐waves. Thanks to the boundary of the deformed half‐plane and some reduced equations, these eventual eigenmodes must locally vanish. Adapting to our case a unique continuation principle for the elasticity system, we conclude that these eigenmodes vanish everywhere. Copyright © 2002 John Wiley & Sons, Ltd.