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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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Volume 27, Issue 1

Issues

The enclosure method for inverse obstacle scattering over a finite time interval: V. Using time-reversal invariance

Masaru IkehataORCID iD: https://orcid.org/0000-0002-1710-5146
Published Online: 2018-12-18 | DOI: https://doi.org/10.1515/jiip-2018-0046

Abstract

The wave equation is time-reversal invariant. The enclosure method, using a Neumann data generated by this invariance, is introduced. The method yields the minimum ball that is centered at a given arbitrary point and encloses an unknown obstacle embedded in a known bounded domain from a single point on the graph of the so-called response operator on the boundary of the domain over a finite time interval. The occurrence of the lacuna in the solution of the free space wave equation is positively used.

Keywords: Enclosure method; time-reversal invariance; inverse obstacle problem; wave equation; non-destructive testing

MSC 2010: 35R30; 35L05

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About the article

Received: 2018-05-17

Revised: 2018-11-23

Accepted: 2018-11-23

Published Online: 2018-12-18

Published in Print: 2019-02-01


Funding Source: Japan Society for the Promotion of Science

Award identifier / Grant number: 17K05331

Award identifier / Grant number: 18H01126

The author was partially supported by Grant-in-Aid for Scientific Research (C) (No. 17K05331) and (B) (No. 18H01126) of Japan Society for the Promotion of Science.


Citation Information: Journal of Inverse and Ill-posed Problems, Volume 27, Issue 1, Pages 133–149, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2018-0046.

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