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Zapiski Nauchnykh Seminarov POMI, 2017, Volume 461, Pages 212–231 (Mi znsl6489)  
This article is cited in 1 scientific paper (total in 1 paper)

On an inverse dynamic problem for the wave equation with a potential on a real line

A. S. Mikhaylova, V. S. Mikhaylovb

a St. Petersburg Department of the Steklov Mathematical Institute, Fontanka 27, 191023, St. Petersburg, Russia
b St. Petersburg State University, 7/9 Universitetskaya nab., 199034 St. Petersburg, Russia
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Abstract: We consider the inverse dynamic problem for the wave equation with a potential on a real line. The forward initial-boundary value problem is set up with a help of boundary triplets. As an inverse data we use an analog of a response operator (dynamic Dirichlet-to-Neumann map). We derive equations of inverse problem and also point out the relationship between dynamic inverse problem and spectral inverse problem from a matrix-valued measure.
Key words and phrases: inverse problem, Schrödinger operator, wave equation, Boundary Control method, boundary triplets.
Funding agency Grant number
Russian Science Foundation 17-11-01064
A. S. Mikhaylov and V. S. Mikhaylov were partly supported by RSF 17-11-01064.
Received: 08.10.2017
English version:
Journal of Mathematical Sciences (New York), 2019, Volume 238, Issue 5, Pages 701–714
DOI: https://doi.org/10.1007/s10958-019-04268-z
Document Type: Article
UDC: 517
Language: English
Citation: A. S. Mikhaylov, V. S. Mikhaylov, “On an inverse dynamic problem for the wave equation with a potential on a real line”, Mathematical problems in the theory of wave propagation. Part 47, Zap. Nauchn. Sem. POMI, 461, POMI, St. Petersburg, 2017, 212–231; J. Math. Sci. (N. Y.), 238:5 (2019), 701–714
Citation in format AMSBIB
\Bibitem{MikMik17}
\by A.~S.~Mikhaylov, V.~S.~Mikhaylov
\paper On an inverse dynamic problem for the wave equation with a~potential on a~real line
\inbook Mathematical problems in the theory of wave propagation. Part~47
\serial Zap. Nauchn. Sem. POMI
\yr 2017
\vol 461
\pages 212--231
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6489}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2019
\vol 238
\issue 5
\pages 701--714
\crossref{https://doi.org/10.1007/s10958-019-04268-z}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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