Far Eastern Mathematical Journal

To content of the issue


Control problems for the MGD model of viscous heat-conducting fluid under mixed boundary conditions


R. V. Brizitskii

2004, issue 2, P. 226–238


Abstract
The control problems for the stationary equations of magnetic hydrodynamics of viscous heat-conducting fluid under mixed boundary conditions for velocity and electric and magnetic fields are considered. The regularity of Lagrange multipliers for the considered control problems is proved. The sufficient conditions of uniqueness of solutions of control problem for specific coast functional are obtained.

Keywords:
magnetic hydrodynamics, heat-conducting fluid, control problem

Download the article (PDF-file)

References

[1] G. V. Alekseev, R. V. Brizickij, Zadachi upravleniya dlya stacionarnyx uravnenij magnitnoj gidrodinamiki vyazkoj teploprovodnoj zhidkosti so smeshannymi granichnymi usloviyami, Preprint № 2 IPM DVO RAN, Dal'nauka, Vladivostok, 2004, 40 s.
[2] A. J. Meir, P. G. Schmidt, “On electromagnetically and thermally driven liquid-metall flows”, Nonlinear Analysis, 47 (2001), 3281–3294.
[3] H. M. Park, W. S. Jung, “Numerical solution of optimal magnetic suppression of natural convection in magneto-hydrodynamic flows by empirical reduction of modes”, Computers Fluids, 31 (2002), 309–334.
[4] G. V. Alekseev, R. V. Brizickij, “Razreshimost' obratnyx e'kstremal'nyx zadach dlya stacionarnyx uravnenij magnitnoj gidrodinamiki vyazkoj zhidkosti so smeshannymi granichnymi usloviyami”, Dal'nevost. mat. zh., 4:1 (2003), 108–126.
[5] A. J. Meir, “The equations of stationary, incompressible magnetohydrodynamics with mixed boundary conditions”, Comp. Math. Applic., 25 (1993), 13–29.
[6] G. V. Alekseev, “Razreshimost' zadach upravleniya dlya stacionarnyx uravnenij magnitnoj gidrodinamiki vyazkoj zhidkosti”, Sib. mat. zhurn., 45:2 (2004), 243–262.
[7] G. V. Alekseev and A. B. Smishliaev, “Solvability of the boundary-value problems for the Boussinesq equations with inhomogeneous boundary conditions”, J. Math. Fluid Mech., 3:1 (2001), 18–39.
[8] G. V. Alekseev, A. B. Smyshlyaev, D. A. Tereshko, “Razreshimost' kraevoj zadachi dlya stacionarnyx uravnenij teplomassoperenosa pri smeshannyx kraevyx usloviyax”, Zh. vychisl. matem. i matem. fiz., 43:1 (2003), 84–98.
[9] G V. Alekseev, “Razreshimost' obratnyx e'kstremal'nyx zadach dlya stacionarnyx uravnenij teplomassoperenosa”, Sib. mat. zhurn., 42:5 (2001), 971–991.
[10] V. Girault, P. A. Raviart, Finite element methods for Navier-Stokes equations, Theory and algorithms, Springer-Verlag, Berlin, 1986.
[11] A. Valli, Orthogonal decompositions of $L^2(\Omega)^3$, Preprint UTM 493, Department of Mathematics. University of Toronto, Galamen, 1995.
[12] P. Grisvard, Elliptic problems in nonsmooth domains, Monograph and studies in mathematics, Pitman, London, 1985.
[13] A. D. Ioffe, V. M. Tixomirov, Teoriya e'kstremal'nyx zadach, Nauka, M., 1974.

To content of the issue