The fixed angle scattering problem and wave equation inverse problems with two measurements
Rakesh, R., & Salo, M. (2020). The fixed angle scattering problem and wave equation inverse problems with two measurements. Inverse Problems, 36(3), Article 035005. https://doi.org/10.1088/1361-6420/ab23a2
Published inInverse Problems
DisciplineInversio-ongelmien huippuyksikköMatematiikkaCentre of Excellence in Inverse ProblemsMathematics
© 2019 IOP Publishing Ltd
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.
PublisherInstitute of Physics
ISSN Search the Publication Forum0266-5611
Publication in research information system
MetadataShow full item record
Related funder(s)Academy of Finland; European Commission
Funding program(s)Academy Project, AoF; Centre of Excellence, AoF
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 fundingSuomen Akatemia 284715, 309963; European Commission 770924
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