The transmission problem in linear isotropic elasticity
Analysis of PDEs
2021-06-02 v3
Abstract
We study the isotropic elastic wave equation in a bounded domain with boundary with coefficients having jumps at a nested set of interfaces satisfying the natural transmission conditions there. We analyze in detail the microlocal behavior of such solution like reflection, transmission and mode conversion of S and P waves, evanescent modes, Rayleigh and Stoneley waves. In particular, we recover Knott's equations in this setting. We show that knowledge of the Dirichlet-to-Neumann map determines uniquely the speed of the P and the S waves if there is a strictly convex foliation with respect to them, under an additional condition of lack of full internal reflection of some of the waves.
Cite
@article{arxiv.1904.03842,
title = {The transmission problem in linear isotropic elasticity},
author = {Plamen Stefanov and Gunther Uhlmann and Andras Vasy},
journal= {arXiv preprint arXiv:1904.03842},
year = {2021}
}