Recovering a bounded elastic body by electromagnetic far-field measurements

Tielei Zhu; Jiaqing Yang; Bo Zhang

doi:10.3934/ipi.2022012

Article Contents

2022, Volume 16, Issue 5: 1063-1083. Doi: 10.3934/ipi.2022012

This issue Previous Article Reconstruction of singularities in two-dimensional quasi-linear biharmonic operator Next Article Photoacoustic tomography in attenuating media with partial data

Recovering a bounded elastic body by electromagnetic far-field measurements

1.
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, China
2.
LSEC and Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China
3.
School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

^*Corresponding author: Jiaqing Yang
^*Corresponding author: Jiaqing Yang

Received: September 30, 2021

Revised: January 31, 2022

Early access: March 2022

Published: October 2022

J. Yang is supported in part by the NNSF of China grant No. 12122114 and The Young Talent Support Plan of Xi'an Jiaotong University

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Abstract

This paper is concerned with the scattering of a time-harmonic electromagnetic wave by a three-dimensional elastic body. The general transmission conditions are considered to model the interaction between the electromagnetic field and the elastic body on the interface by Voigt's model. The existence of a unique solution is first proved in an appropriate Sobolev space by employing the variational method with the classical Fredholm alternative. The inverse problem is then investigated to recover the elastic body by the scattered wave-field data. It is shown that the shape and location of the body is uniquely determined by the fixed energy magnetic (or electric) far-field measurements corresponding to incident plane waves with all polarizations.

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Mathematics Subject Classification: Primary: 74F15; Secondary: 35Q60, 78A45.

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Figure 1. Interaction between electromagnetic wave and a bounded elastic body

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Figure 2. Two different elastic bodies

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