A1 Journal article (refereed)
The fixed angle scattering problem and wave equation inverse problems with two measurements (2020)


Rakesh, R.; Salo, M. (2020). The fixed angle scattering problem and wave equation inverse problems with two measurements. Inverse Problems, 36 (3), 035005. DOI: 10.1088/1361-6420/ab23a2


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Publication details

All authors or editors: Rakesh, R.; Salo, M.

Journal or series: Inverse Problems

ISSN: 0266-5611

eISSN: 1361-6420

Publication year: 2020

Volume: 36

Issue number: 3

Article number: 035005

Publisher: Institute of Physics

Publication country: United Kingdom

Publication language: English

DOI: https://doi.org/10.1088/1361-6420/ab23a2

Open Access: Publication channel is not openly available

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/66712

Publication is parallel published: https://arxiv.org/abs/1901.05402


Abstract

We consider two formally determined inverse problems for the wave equation in more than one space dimension. Motivated by the fixed angle inverse scattering problem, we show that a compactly supported potential is uniquely determined by the far field pattern generated by plane waves coming from exactly two opposite directions. This implies that a reflection symmetric potential is uniquely determined by its fixed angle scattering data. We also prove a Lipschitz stability estimate for an associated problem. Motivated by the point source inverse problem in geophysics, we show that a compactly supported potential is
uniquely determined from boundary measurements of the waves generated by exactly two sources - a point source and an incoming spherical wave. These results are proved by using Carleman estimates and adapting the ideas introduced by Bukhgeim and Klibanov on the use of Carleman estimates for inverse problems.


Keywords: inverse problems


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Ministry reporting: Yes

Reporting Year: 2020

Preliminary JUFO rating: 2


Last updated on 2020-18-08 at 13:13