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
Contributing organizations
Related projects
- Centre of Excellence in Inverse Problems Research
- Salo, Mikko
- Research Council of Finland
- Inverse boundary problems: toward a unified theory
- Salo, Mikko
- Research Council of Finland
- Inverse boundary problems - toward a unified theory
- Salo, Mikko
- European Commission
Ministry reporting: Yes
VIRTA submission year: 2020
JUFO rating: 2