# American Institute of Mathematical Sciences

doi: 10.3934/ipi.2020075

## The interior transmission eigenvalue problem for elastic waves in media with obstacles

 1 Department of Mathematics, Rutgers University, New Brunswick, USA 2 Department of Mathematics, National Taiwan University, Taipei 106, Taiwan 3 Institute of Applied Mathematical Sciences, NCTS, National Taiwan University, Taipei 106, Taiwan

* Corresponding author: Pu-Zhao Kow

Received  June 2020 Revised  September 2020 Published  November 2020

In this paper, we investigate the interior transmission eigenvalue problem for elastic waves propagating outside a sound-soft or a sound-hard obstacle surrounded by an anisotropic layer. This study is motivated by the inverse problem of identifying an object embedded in an inhomogeneous media in the presence of elastic waves. Our analysis of this non-selfadjoint eigenvalue problem relies on the weak formulation of involved boundary value problems and some fundamental tools in functional analysis.

Citation: Fioralba Cakoni, Pu-Zhao Kow, Jenn-Nan Wang. The interior transmission eigenvalue problem for elastic waves in media with obstacles. Inverse Problems & Imaging, doi: 10.3934/ipi.2020075
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Plot of $F(k)$ in (21) with $\mu = 1$, $\lambda = 1$ and $n = 1/2$ (GNU Octave)
Plot of $F(k)$ in (22) with $\mu = 1$, $\lambda = 1$ and $n = 1/2$ (GNU Octave)
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