Reconstruction of a source domain from the Cauchy data: II. Three-dimensional case. (2nd November 2021)

• Record Type: Journal Article
• Authors: Ikehata, Masaru
• Is Part Of: Inverse problems. Volume 37:Number 12(2021)
• Publication Date: 2021-11-02
• Subjects: exponentially growing solutions -- enclosure method -- inverse source problem -- inverse obstacle problem -- Helmholtz equation -- circular cone singularity; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac2fb9
• Languages: English
• ISSNs: 0266-5611

Abstract

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.