Abstract:
Control problems for a steady-state model of the magnetohydrodynamics of a viscous incompressible fluid in a bounded domain with an impermeable, perfectly conducting boundary are formulated. The resolvability of the problems is studied, the use of the Lagrange principle is justified, and optimality systems are analyzed.
Keywords:
magnetohydrodynamics, viscous fluid, control problems.
Citation:
G. V. Alekseev, “Control problems for the steady-state equations of magnetohydrodynamics of a viscous incompressible fluid”, Prikl. Mekh. Tekh. Fiz., 44:6 (2003), 170–179; J. Appl. Mech. Tech. Phys., 44:6 (2003), 890–899
\Bibitem{Ale03}
\by G.~V.~Alekseev
\paper Control problems for the steady-state equations of magnetohydrodynamics of a viscous incompressible fluid
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2003
\vol 44
\issue 6
\pages 170--179
\mathnet{http://mi.mathnet.ru/pmtf2571}
\elib{https://elibrary.ru/item.asp?id=17274863}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2003
\vol 44
\issue 6
\pages 890--899
\crossref{https://doi.org/10.1023/A:1026256325488}
Linking options:
https://www.mathnet.ru/eng/pmtf2571
https://www.mathnet.ru/eng/pmtf/v44/i6/p170
This publication is cited in the following 12 articles:
Gennadii Alekseev, Yuliya Spivak, “Stability Estimates of Optimal Solutions for the Steady Magnetohydrodynamics-Boussinesq Equations”, Mathematics, 12:12 (2024), 1912
Gennadii Alekseev, “Analysis of Control Problems for Stationary Magnetohydrodynamics Equations under the Mixed Boundary Conditions for a Magnetic Field”, Mathematics, 11:12 (2023), 2610
Gennady Alekseev, Roman Brizitskii, “Control problems for the stationary MHD equations under mixed boundary conditions”, J. Phys.: Conf. Ser., 1268:1 (2019), 012005
Andrey Yu. Fershalov, Mikhail Yu. Fershalov, Yuriy Ya. Fershalov, Timofey V. Sazonov, Damir I. Ibragimov, “Research Data of Turbine Nozzles of 5-9 Degree Outlet Angles”, AMM, 770 (2015), 547
Andrey Yu. Fershalov, Mikhail Yu. Fershalov, Yuriy Ya. Fershalov, Timofey V. Sazonov, “Results of the Study Rotor Wheels Supersonic Microturbines with a Large Angle of Rotation of the Flow”, AMM, 752-753 (2015), 884
Andrey Yu. Fershalov, Mikhail Yu. Fershalov, Yuriy Ya. Fershalov, Timofey V. Sazonov, Damir I. Ibragimov, “The Design of the Nozzle for the Nozzle Box Microturbines”, AMM, 789-790 (2015), 205
Andrey Yu. Fershalov, Yuriy Ya. Fershalov, Mikhail Yu. Fershalov, Timofey V. Sazonov, Damir I. Ibragimov, “Analysis and Optimization of Efficiency Rotor Wheels Microturbines”, AMM, 635-637 (2014), 76
G. V. Alekseev, R. V. Brizitskii, V. V. Pukhnachev, “Solvability of the inhomogeneous mixed boundary value problem for stationary magnetohydrodynamic equations”, Dokl. Phys., 59:10 (2014), 467
G. Alekseev, R. Brizitskii, “Solvability of the boundary value problem for stationary magnetohydrodynamic equations under mixed boundary conditions for the magnetic field”, Applied Mathematics Letters, 32 (2014), 13
Roman Brizitskii, Dmitry Tereshko, “Control Problems for the MHD Equations under Inhomogeneous Mixed Boundary Conditions”, AMM, 670-671 (2014), 626
Max Gunzburger, Catalin Trenchea, “Analysis of an optimal control problem for the three-dimensional coupled modified Navier–Stokes and Maxwell equations”, Journal of Mathematical Analysis and Applications, 333:1 (2007), 295
R. V. Brizitskii, D. A. Tereshko, “On the solvability of boundary value problems for the stationary magnetohydrodynamic equations with inhomogeneous mixed boundary conditions”, Diff Equat, 43:2 (2007), 246
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