Reconstruction of penetrable obstacles in the anisotropic acoustic scattering

Yi-Hsuan  Lin

doi:10.3934/ipi.2016020

Article Contents

2016, Volume 10, Issue 3: 765-780. Doi: 10.3934/ipi.2016020

This issue Previous Article Lavrentiev's regularization method in Hilbert spaces revisited Next Article A gradient-based method for atmospheric tomography

Reconstruction of penetrable obstacles in the anisotropic acoustic scattering

Yi-Hsuan Lin^1,

1.
Department of Mathematics, National Taiwan University, Taipei 106

Received: January 31, 2015

Revised: March 31, 2016

Published: July 2016

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Abstract

We develop an enclosure-type reconstruction scheme to identify penetrable obstacles in acoustic waves with anisotropic medium in $\mathbb{R}^{3}$. The main difficulty of treating this problem lies in the fact that there are no complex geometrical optics solutions available for the acoustic equation with anisotropic medium in $\mathbb{R}^{3}$. Instead, we will use another type of special solutions called oscillating-decaying solutions. Even though that oscillating-decaying solutions are defined only on the half space, we are able to give necessary boundary inputs by the Runge approximation property. Moreover, since we are considering a Helmholtz-type equation, we turn to Meyers' $L^{p}$ estimate to compare the integrals coming from oscillating-decaying solutions and those from reflected solutions.

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Mathematics Subject Classification: Primary: 35R30; Secondary: 35J15.

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