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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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Volume 25, Issue 2

Issues

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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/ 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(q,a) arisen from acoustic scattering problems was considered. The authors showed that q(x) on the interval [0,1] can be uniquely determined by the interior twin-dense nodal subset WT([0,1]), or WT([a0,1]), respectively. Using the above results, two uniqueness theorems of the spherically symmetric speed of sound η(r) for acoustic scattering problems are obtained.

Keywords: Inverse nodal problem; transmission eigenvalue problem; twin-dense nodal set; potential

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

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About the article

Received: 2016-03-22

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, DOI: https://doi.org/10.1515/jiip-2016-0021.

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