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 editorsRakesh; Salo, Mikko

Journal or seriesSIAM Journal on Mathematical Analysis



Publication year2020


Issue number6

Pages range5467-5499

PublisherSociety for Industrial & Applied Mathematics (SIAM)

Publication countryUnited States

Publication languageEnglish


Publication open accessNot 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


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.

Keywordsinverse problemspartial differential equations

Free keywordsfixed angle; inverse scattering; plane wave; scattering amplitude

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Ministry reportingYes

Reporting Year2020

JUFO rating2

Last updated on 2024-22-04 at 11:47