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arXiv · 2107.05232

Reconstruction of a source domain from the Cauchy data: II. Three dimensional case

Masaru Ikehata
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Abstract

This paper is concerned with reconstruction issue of some typical inverse problems and consists of three parts. First a framework of the enclosure method for an inverse source problem governed by the Helmholtz equation at a fixed wave number in three dimensions is introduced. It is based on the nonvanishing of the coefficient of the leading profile of an oscillatory integral over a domain having a conical singularity. Second an explicit formula of the coefficient for a domain having a circular cone singularity and its implication under the framework are given. Third, an application under the framework to an inverse obstacle problem governed by an inhomogeneous Helmholtz equation at a fixed wave number in three dimensions is given.

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Masaru Ikehata. 2021-07-12. Reconstruction of a source domain from the Cauchy data: II. Three dimensional case. https://doi.org/10.1088/1361-6420%2Fac2fb9

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