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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2021, Volume 18, Issue 2, Pages 827–833
DOI: https://doi.org/10.33048/semi.2021.18.061 (Mi semr1403) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Differentical equations, dynamical systems and optimal control

Reconstruction of a high-frequency source term of the wave equation from the asymptotics of the solution. Case of the Cauchy problem

E. V. Korablina, V. B. Levenshtam

Steklov Mathematical Institute of the Russian Academy of Sciences, 8, Gubkin str., Moscow, 119991, Russia
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DOI: https://doi.org/10.33048/semi.2021.18.061
Abstract: We consider The Cauchy problem for the wave equation with an unknown right hand side, that rapidly oscillates in time. This right hand side is reconstructed from the three-term asymptotics of a solution, which are given at one point of the domain. In this case, an approach developed earlier by one of the authors of this article is used to solve the inverse problems with rapidly oscillating data.
Keywords: wave equation, Cauchy problem, asymptotics of a solution, reconstruction of an unknown high-frequency source term.
Funding agency Grant number
Russian Science Foundation 20-11-20141
Thie research is supported by a grant from the Russian Science Foundtaion (project No. 20-11-20141).
Received April 28, 2021, published July 25, 2021
Bibliographic databases:
Document Type: Article
UDC: 517.955.8
MSC: 35C20
Language: English
Citation: E. V. Korablina, V. B. Levenshtam, “Reconstruction of a high-frequency source term of the wave equation from the asymptotics of the solution. Case of the Cauchy problem”, Sib. Èlektron. Mat. Izv., 18:2 (2021), 827–833
Citation in format AMSBIB
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\by E.~V.~Korablina, V.~B.~Levenshtam
\paper Reconstruction of a high-frequency source term of the wave equation from the asymptotics of the solution. Case of the Cauchy problem
\jour Sib. \`Elektron. Mat. Izv.
\yr 2021
\vol 18
\issue 2
\pages 827--833
\mathnet{http://mi.mathnet.ru/semr1403}
\crossref{https://doi.org/10.33048/semi.2021.18.061}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4292562}
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