Fixed Angle Inverse Scattering for Almost Symmetric or Controlled Perturbations
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
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SIAM Journal on Mathematical AnalysisDate
2020Discipline
Inversio-ongelmien huippuyksikköMatematiikkaCentre of Excellence in Inverse ProblemsMathematicsCopyright
© 2020 Society for Industrial & Applied Mathematics (SIAM)
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.
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Society for Industrial & Applied Mathematics (SIAM)ISSN Search the Publication Forum
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https://converis.jyu.fi/converis/portal/detail/Publication/47362747
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Related funder(s)
Research Council of Finland; European CommissionFunding program(s)
Centre of Excellence, AoF; Academy Project, AoF; ERC Consolidator Grant
The content of the publication reflects only the author’s view. The funder is not responsible for any use that may be made of the information it contains.
Additional information about funding
The work of the first author was supported by the National Science Foundation grant DMS-1615616. The work of the second author was supported by the Academy of Finland grants 284715, 309963 and the European Research Council under Horizon 2020 grant ERC CoG 770924.License
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