On recovery of an inhomogeneous cavity in inverse acoustic scattering

Fenglong Qu; Jiaqing Yang

doi:10.3934/ipi.2018012

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2018, Volume 12, Issue 2: 281-291. Doi: 10.3934/ipi.2018012

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On recovery of an inhomogeneous cavity in inverse acoustic scattering

Fenglong Qu^1, and
Jiaqing Yang^2, ,

1.
School of Mathematics and Informational Science, Yantai University, Yantai, Shandong 264005, China
2.
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China

* The corresponding author
* The corresponding author

Received: August 2016

Revised: December 2017

Published: April 2018

Fenglong Qu is supported by the NNSF of China under grant No. 11401513 and NSF of Shandong Province of China grant No. ZR2017MA044. Jiaqing Yang is supported by the NNSF of China under grant No. 11401568 and No. 11771349, by the China Postdoctoral Science Foundation under grant No. 2015M580827 and No. 2016T90900, and by Postdoctoral research project of Shaanxi Province of China under grant No. 2016BSHYDZZ52.

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Abstract

Consider the time-harmonic acoustic scattering of an incident point source inside an inhomogeneous cavity. By constructing an equivalent integral equation, the well-posedness of the direct problem is proved in $L^p$ with using the classical Fredholm theory. Motivated by the previous work [10], a novel uniqueness result is then established for the inverse problem of recovering the refractive index of piecewise constant function from the wave fields measured on a closed surface inside the cavity.

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Mathematics Subject Classification: Primary: 35R30, 35P25; Secondary: 78A46.

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Figure 1. The inhomogeneous cavity

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