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 Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 144–157 (Mi semr1045)

Differentical equations, dynamical systems and optimal control

Inverse problems for a mixed parabolic-hyperbolic equation with a degenerate parabolic part

S. N. Sidorov

Sterlitamak branch of the Institute of Strategic Studies of the Republic of Bashkortostan, 68, Odesskaya str., Sterlitamak, 453103, Russia

Abstract: In this paper, inverse problems are posed and studied to determine the factors of the right-hand sides of a mixed parabolic-hyperbolic type with a degenerate parabolic part, depending on time. On the basis of the theory of integral equations, the corresponding uniqueness theorems and the existence of solutions of inverse problems were proved, and explicit formulas for the solution were obtained.

Keywords: equation of mixed parabolic-hyperbolic type, initial-boundary value problem, inverse problems, uniqueness, existence, series, small denominators, integral equations.

DOI: https://doi.org/10.33048/semi.2019.16.007

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Document Type: Article
UDC: 517.95
MSC: 35M10+35R30
Received November 30, 2018, published January 31, 2019

Citation: S. N. Sidorov, “Inverse problems for a mixed parabolic-hyperbolic equation with a degenerate parabolic part”, Sib. Èlektron. Mat. Izv., 16 (2019), 144–157

Citation in format AMSBIB
\Bibitem{Sid19} \by S.~N.~Sidorov \paper Inverse problems for a mixed parabolic-hyperbolic equation with a degenerate parabolic part \jour Sib. \Elektron. Mat. Izv. \yr 2019 \vol 16 \pages 144--157 \mathnet{http://mi.mathnet.ru/semr1045} \crossref{https://doi.org/10.33048/semi.2019.16.007} `