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Zap. Nauchn. Sem. POMI, 2018, Volume 477, Pages 54–86 (Mi znsl6737)  

Optimal feedback control problem for the Bingam model with periodical boundary conditions on spatial variables

V. G. Zvyagin, A. V. Zvyagin, M. V. Turbin

Voronezh State University, Voronezh, Russia

Abstract: The paper is devoted to an optimal feedback control problem for Bingham model with periodic conditions on spatial variables. It is given an interpretation of the considered feedback control problem in the form of an operator inclusion with a multi-valued right-hand side. On the base of the topological approximation approach to the study of hydrodynamics problems and the degree theory of multivalued vector fields, the solutions existence of this inclusion is proved. Then it is proved that among the solutions of the considered problem there is a solution which minimizes to a given quality functional.

Key words and phrases: Bingham model, optimal feedback control problem, topological approximation approach, existence theorem, degree of multi-valued vector fields.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 14.Z50.31.0037
МК-2213.2018.1


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Received: 29.11.2018

Citation: V. G. Zvyagin, A. V. Zvyagin, M. V. Turbin, “Optimal feedback control problem for the Bingam model with periodical boundary conditions on spatial variables”, Boundary-value problems of mathematical physics and related problems of function theory. Part 47, Zap. Nauchn. Sem. POMI, 477, POMI, St. Petersburg, 2018, 54–86

Citation in format AMSBIB
\Bibitem{ZvyZvyTur18}
\by V.~G.~Zvyagin, A.~V.~Zvyagin, M.~V.~Turbin
\paper Optimal feedback control problem for the Bingam model with periodical boundary conditions on spatial variables
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~47
\serial Zap. Nauchn. Sem. POMI
\yr 2018
\vol 477
\pages 54--86
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6737}


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