Tsukuba Journal of Mathematics

An inverse spectral uniqueness in exterior transmission problem

Lung-Hui Chen

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Abstract

We consider an inverse spectral theory in a domain with the cavity in a penetrable inhomogeneous medium. An ODE system is constructed piecewise through the ODE eigenfunctions inside and outside the cavity. Then the ODE system is connected to the PDE system via the analytic continuation property of the Helmholtz equation. For each scattered angle, we describe its eigenvalue density in the complex plane, and prove an inverse uniqueness on the inhomogeneity by the measurements in the far-fields. We take advantage of the symmetry near infinity.

Article information

Source
Tsukuba J. Math., Volume 41, Number 2 (2017), 297-312.

Dates
Received: 5 July 2017
Revised: 12 October 2017
First available in Project Euclid: 21 March 2018

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1521597627

Digital Object Identifier
doi:10.21099/tkbjm/1521597627

Mathematical Reviews number (MathSciNet)
MR3778317

Zentralblatt MATH identifier
06857026

Subjects
Primary: 35P10: Completeness of eigenfunctions, eigenfunction expansions 35P25: Scattering theory [See also 47A40] 35Q60: PDEs in connection with optics and electromagnetic theory 35R30: Inverse problems 34B24: Sturm-Liouville theory [See also 34Lxx]

Keywords
inverse scattering theory inverse problem Sturm-Liouville theory exterior transmission problem Cartwright-Levinson theory spectral flaw of ODE

Citation

Chen, Lung-Hui. An inverse spectral uniqueness in exterior transmission problem. Tsukuba J. Math. 41 (2017), no. 2, 297--312. doi:10.21099/tkbjm/1521597627. https://projecteuclid.org/euclid.tkbjm/1521597627


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