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 J. Comp. Eng. Math., 2016, Volume 3, Issue 2, Pages 57–67 (Mi jcem64)

Computational Mathematics

Optimal control of solutions to the initial-final problem for the Sobolev type equation of higher order

A. A. Zamyshlyaeva, O. N. Tsyplenkova, E. V. Bychkov

South Ural State University, Chelyabinsk, Russian Federation

Abstract: Of concern is the optimal control problem for the Sobolev type higher order equation with relatively polynomially bounded operator pencil. The theorem of existence and uniqueness of strong solutions to the initial-final problem for abstract equation is proved. The sufficient conditions for optimal control existence and uniqueness of such solutions are found. We use the ideas and methods developed by G.A. Sviridyuk and his disciples.

Keywords: Sobolev type equations, relatively polynomially bounded operator pencil, strong solutions, optimal control.

DOI: https://doi.org/10.14529/jcem1602007

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Bibliographic databases:

UDC: 517.9
MSC: 35Q93, 34H05
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Citation: A. A. Zamyshlyaeva, O. N. Tsyplenkova, E. V. Bychkov, “Optimal control of solutions to the initial-final problem for the Sobolev type equation of higher order”, J. Comp. Eng. Math., 3:2 (2016), 57–67

Citation in format AMSBIB
\Bibitem{ZamTsyByc16} \by A.~A.~Zamyshlyaeva, O.~N.~Tsyplenkova, E.~V.~Bychkov \paper Optimal control of solutions to the initial-final problem for the Sobolev type equation of higher order \jour J. Comp. Eng. Math. \yr 2016 \vol 3 \issue 2 \pages 57--67 \mathnet{http://mi.mathnet.ru/jcem64} \crossref{https://doi.org/10.14529/jcem1602007} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3527957} \zmath{https://zbmath.org/?q=an:1356.49006} \elib{http://elibrary.ru/item.asp?id=26399838}