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December 2017 An inverse spectral uniqueness in exterior transmission problem
Lung-Hui Chen
Tsukuba J. Math. 41(2): 297-312 (December 2017). DOI: 10.21099/tkbjm/1521597627

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.

Citation

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Lung-Hui Chen. "An inverse spectral uniqueness in exterior transmission problem." Tsukuba J. Math. 41 (2) 297 - 312, December 2017. https://doi.org/10.21099/tkbjm/1521597627

Information

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

zbMATH: 06857026
MathSciNet: MR3778317
Digital Object Identifier: 10.21099/tkbjm/1521597627

Subjects:
Primary: 34B24, 35P10, 35P25, 35Q60, 35R30

Rights: Copyright © 2017 University of Tsukuba, Institute of Mathematics

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Vol.41 • No. 2 • December 2017
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