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# Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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# Inverse transmission eigenvalue problems with the twin-dense nodal subset

Yu Ping Wang
• Corresponding author
• Department of Applied Mathematics, Nanjing Forestry University, Nanjing, 210037, Jiangsu, P. R. China
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• Other articles by this author:
/ Chung Tsun Shieh
/ Hong Yi Miao
Published Online: 2016-07-12 | DOI: https://doi.org/10.1515/jiip-2016-0021

## Abstract

The inverse nodal problem for the Sturm–Liouville operator $L\left(q,a\right)$ arisen from acoustic scattering problems was considered. The authors showed that $q\left(x\right)$ on the interval $\left[0,1\right]$ can be uniquely determined by the interior twin-dense nodal subset ${W}_{T}\left(\left[0,1\right]\right)$, or ${W}_{T}\left(\left[{a}_{0},1\right]\right)$, respectively. Using the above results, two uniqueness theorems of the spherically symmetric speed of sound $\eta \left(r\right)$ for acoustic scattering problems are obtained.

MSC 2010: 34A55; 34L40; 35R30; 35Q60; 35J40

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Revised: 2016-05-18

Accepted: 2016-05-27

Published Online: 2016-07-12

Published in Print: 2017-04-01

Citation Information: Journal of Inverse and Ill-posed Problems, Volume 25, Issue 2, Pages 237–249, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219,

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