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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2022, Volume 208, Pages 29–36
DOI: https://doi.org/10.36535/0233-6723-2022-208-29-36 (Mi into992) 		 
Asymptotic problem of restoring the high-frequency right-hand side of the telegraph equation

E. V. Korablinaab, V. B. Levenshtamba

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Southern Federal University, Rostov-on-Don
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DOI: https://doi.org/10.36535/0233-6723-2022-208-29-36
Abstract: In this paper, we consider the Cauchy problem for the telegraph equation. The lower coefficient and the right-hand side of the equation oscillate in time with a high frequency, the amplitude of the lower coefficient is small, namely, is inversely proportional to the frequency, and the right-hand side is unknown. We examine the problem on the recovery of the right-hand side from the three-term asymptotics of the solution given at some point in space. For this purpose, we use a nonclassical algorithm for solving inverse coefficient problems with rapidly oscillating data.
Keywords: inverse problem, asymptotic methods, telegraph equation, rapidly oscillating data.
Funding agency Grant number
Russian Science Foundation 20-11-20141
This work was supported by the Russian Science Foundation (project No. 20-11-20141).
Document Type: Article
UDC: 517.928
MSC: 34D05
Language: Russian
Citation: E. V. Korablina, V. B. Levenshtam, “Asymptotic problem of restoring the high-frequency right-hand side of the telegraph equation”, Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 1, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 208, VINITI, Moscow, 2022, 29–36
Citation in format AMSBIB
\Bibitem{KorLev22}
\by E.~V.~Korablina, V.~B.~Levenshtam
\paper Asymptotic problem of restoring the high-frequency right-hand side of the telegraph equation
\inbook Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 1
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2022
\vol 208
\pages 29--36
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into992}
\crossref{https://doi.org/10.36535/0233-6723-2022-208-29-36}
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