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Abstracts

The goal of the paper is the theoretical study of inverse extremum problems for the stationary models of magneto-hydrodynamics of viscous thermally conducting fluid.

The control of flows of viscous incompressible electrically and thermally conducting fluids for the purpose of achieving some desired objectives plays an important role in applied fields of magnetic hydrodynamics, including creation of the nuclear reactor cooling systems, development of the crystal growth processing technique in the microelectronics industry, creation of the technologies of the contactless electromagnetic stirring of metallic melts in the casting industry, the design of new submarine propulsion devices. The study of the influence of the magnetic field to the convection development is one of the purposes of modeling when using MHD models. In a number of cases such as nuclear reactor cooling by liquid metals the magnetic field is used for the convection enhancement. Opposite to in the crystal growth setups it is used for convection suppression in order to improve the crystal quality. The study of the question on possibility of convection suppression or enhancement gives rise to the control problems for the models of MHD. They have the purpose to establish the most efficient techniques of control by thermohydrodynamic processes in a viscous fluid.

In the paper the general technique based on papers [1-3] is developed for analyzing our control problems. By using this technique the solvability of both the original boundary value problems and the inverse extremum problems for a fairly wide class of weakly lower semicontinous quality functionals is proved and sufficient conditions are established which provide the uniqueness and regularity of solutions. Details can be found in [4].

This work was supported by Russian Foundation of Basic Research under grant № 04-01-00136.

References

1. G.V. Alekseev, The control problems for the steady - state equations of magnetohydrodynamics of a viscous incompressible fluid. J. Appl. Mech. Tech. Phys. (2003) 44, No. 6, 890 - 899.

2. G.V. Alekseev, Solvability of control problems for the stationary equations of viscous magnetic hydrodynamics. Sib. Math. J. (2004) 45, No. 2, 197 - 213.

3. G.V. Alekseev, Control problems for stationary equations of magnetic hydrodynamics. Dokl. Math. (2004) 69, No. 2, 310-313.

4. G.V. Alekseev, Theoretical analysis of control problems for the stationary models of magnetic hydrodynamics of viscous thermally conducting fluid. Preprint N1 IAM FEB RAS. DalNauka. 2004.

Note. Abstracts are published in author's edition

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