# American Institute of Mathematical Sciences

April  2018, 12(2): 281-291. doi: 10.3934/ipi.2018012

## On recovery of an inhomogeneous cavity in inverse acoustic scattering

 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

Received  August 2016 Revised  December 2017 Published  February 2018

Fund Project: 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.

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.

Citation: Fenglong Qu, Jiaqing Yang. On recovery of an inhomogeneous cavity in inverse acoustic scattering. Inverse Problems & Imaging, 2018, 12 (2) : 281-291. doi: 10.3934/ipi.2018012
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##### References:
The inhomogeneous cavity
The inhomogeneous cavity
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