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Eurasian Mathematical Journal, 2023, Volume 14, Number 1, Pages 55–70
DOI: https://doi.org/10.32523/2077-9879-2023-14-1-55-70 (Mi emj462) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On a linear inverse potential problem with approximate data on the potential field on an approximately given surface

E. B. Laneev, E. Yu. Ponomarenko

S.M. Nikol'skii Mathematical Institute, Peoples Friendship University of Russia (RUDN University), 6 Miklukho Maklay St, 117198 Moscow, Russian Federation
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DOI: https://doi.org/10.32523/2077-9879-2023-14-1-55-70
Abstract: An approximate solution of the linear inverse problem for the Newtonian potential for bodies of constant thickness is constructed. The solution is stable with respect to the error in the data on the potential field given on an inaccurately known surface. The problem is reduced to an integral equation of the first kind, the proof of the stability of the solution is based on the Tikhonov regularization method.
Keywords and phrases: ill-posed problem, inverse problem for the potential, Sretenskiy class of bodies, method of Tikhonov regularization.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00610_a
The research is supported by the Russian Foundation for Basic Research (grant No. 20-01-00610a).
Received: 16.01.2022
Bibliographic databases:
Document Type: Article
MSC: 35R25, 35R30
Language: English
Citation: E. B. Laneev, E. Yu. Ponomarenko, “On a linear inverse potential problem with approximate data on the potential field on an approximately given surface”, Eurasian Math. J., 14:1 (2023), 55–70
Citation in format AMSBIB
\Bibitem{LanPon23}
\by E.~B.~Laneev, E.~Yu.~Ponomarenko
\paper On a linear inverse potential problem with approximate data on the potential field on an approximately given surface
\jour Eurasian Math. J.
\yr 2023
\vol 14
\issue 1
\pages 55--70
\mathnet{http://mi.mathnet.ru/emj462}
\crossref{https://doi.org/10.32523/2077-9879-2023-14-1-55-70}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4575860}
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