A1 Journal article (refereed)
Fixed Angle Inverse Scattering for Almost Symmetric or Controlled Perturbations (2020)

Rakesh, Salo, Mikko. (2020). Fixed Angle Inverse Scattering for Almost Symmetric or Controlled Perturbations. SIAM Journal on Mathematical Analysis, 52(6), 5467-5499. https://doi.org/10.1137/20M1319309

JYU authors or editors

Publication details

All authors or editors: Rakesh; Salo, Mikko

Journal or series: SIAM Journal on Mathematical Analysis

ISSN: 0036-1410

eISSN: 1095-7154

Publication year: 2020

Volume: 52

Issue number: 6

Pages range: 5467-5499

Publisher: Society for Industrial & Applied Mathematics (SIAM)

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1137/20M1319309

Publication open access: Not open

Publication channel open access:

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/73371

Web address of parallel published publication (pre-print): https://arxiv.org/abs/1905.03974

Abstract

We consider the fixed angle inverse scattering problem and show that a compactly supported potential is uniquely determined by its scattering amplitude for two opposite fixed angles. We also show that almost symmetric or horizontally controlled potentials are uniquely determined by their fixed angle scattering data. This is done by establishing an equivalence between the frequency domain and the time domain formulations of the problem, and by solving the time domain problem by extending the methods of [Rakesh and M. Salo, Inverse Problems, 36 (2020), 035005] which adapts the ideas introduced in [A. Bukhgeim and M. Klibanov, Soviet Math. Dokl., 24 (1981), pp. 244--247] and [O. Imanuvilov and M. Yamamoto, Comm. Partial Differential Equations, 26 (2001), pp. 1409--1425] on the use of Carleman estimates for inverse problems.

Keywords: inverse problems; partial differential equations

Free keywords: fixed angle; inverse scattering; plane wave; scattering amplitude

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Related projects

Ministry reporting: Yes

Reporting Year: 2020

JUFO rating: 2