Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 141, Pages 111–133 (Mi into248)  
Inverse problems for initial conditions of the mixed problem for the telegraph equation

K. B. Sabitova, A. R. Zaynullovb

a Institute of Applied Research, Sterlitamak
b Sterlitamak Branch of Bashkir State University
Full-text PDF (283 kB)
Abstract: In this paper, we examine inverse problems for initial conditions for the wave and telegraph equations and state uniqueness criteria. Solutions of these problems are constructed in the series form. In the proof of uniform convergence of these series, the problem on small denominators appear. We prove estimates of small denominators separated from zero and obtain asymptotics that allow one to justify the convergence in the class of regular solutions.
Keywords: telegraph equation, inverse problem, Dirichlet problem, mixed boundary conditions, uniqueness criteria, existence, series, small denominators.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-97003-Поволжье
This paper was partially supported by the Russian Foundation for Basix Research (project No. 14-01-97003-Volga region.
English version:
Journal of Mathematical Sciences, 2019, Volume 241, Issue 5, Pages 622–645
DOI: https://doi.org/10.1007/s10958-019-04450-3
Bibliographic databases:
Document Type: Article
UDC: 517.95
MSC: 35M10, 35Q60
Language: Russian
Citation: K. B. Sabitov, A. R. Zaynullov, “Inverse problems for initial conditions of the mixed problem for the telegraph equation”, Differential equations. Spectral theory, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 141, VINITI, M., 2017, 111–133; Journal of Mathematical Sciences, 241:5 (2019), 622–645
Citation in format AMSBIB
\Bibitem{SabZay17}
\by K.~B.~Sabitov, A.~R.~Zaynullov
\paper Inverse problems for initial conditions of the mixed problem for the telegraph equation
\inbook Differential equations. Spectral theory
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 141
\pages 111--133
\publ VINITI
\publaddr M.
\mathnet{http://mi.mathnet.ru/into248}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3801343}
\zmath{https://zbmath.org/?q=an:1423.35455}
\transl
\jour Journal of Mathematical Sciences
\yr 2019
\vol 241
\issue 5
\pages 622--645
\crossref{https://doi.org/10.1007/s10958-019-04450-3}
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