Reconstruction of penetrable obstacles in the anisotropic acoustic scattering

Yi-Hsuan Lin

doi:10.3934/ipi.2016020

Reconstruction of penetrable obstacles in the anisotropic acoustic scattering

Yi-Hsuan Lin^*

^*Corresponding author for this work

Department of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We develop an enclosure-type reconstruction scheme to identify penetrable obstacles in acoustic waves with anisotropic medium in ℝ³. 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 ℝ³. 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 reected solutions.

Original language	English
Pages (from-to)	765-780
Number of pages	16
Journal	Inverse Problems and Imaging
Volume	10
Issue number	3
DOIs	https://doi.org/10.3934/ipi.2016020
State	Published - 1 Aug 2016

Keywords

Enclosure method
Meyers L estimates
Oscillating-decaying solutions
Reconstruction
Runge approximation property

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10.3934/ipi.2016020

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abstract = "We develop an enclosure-type reconstruction scheme to identify penetrable obstacles in acoustic waves with anisotropic medium in ℝ3. 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 ℝ3. 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' Lp estimate to compare the integrals coming from oscillating-decaying solutions and those from reected solutions.",

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N2 - We develop an enclosure-type reconstruction scheme to identify penetrable obstacles in acoustic waves with anisotropic medium in ℝ3. 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 ℝ3. 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' Lp estimate to compare the integrals coming from oscillating-decaying solutions and those from reected solutions.

AB - We develop an enclosure-type reconstruction scheme to identify penetrable obstacles in acoustic waves with anisotropic medium in ℝ3. 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 ℝ3. 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' Lp estimate to compare the integrals coming from oscillating-decaying solutions and those from reected solutions.

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KW - Meyers L estimates

KW - Oscillating-decaying solutions

KW - Reconstruction

KW - Runge approximation property

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Reconstruction of penetrable obstacles in the anisotropic acoustic scattering

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Keywords

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