Boundary Value and Control Problems for the Stationary Magnetic Hydrodynamic Equations of Heat Conducting Fluid with Variable Coefficients

The global solvability and local uniqueness of boundary value problem's solutions for stationary magnetic hydrodynamic equations for heat conducting fluid with variable coefficients are proved. Maximum and minimum principle for temperature is established. Multiplicative control problem for the model under consideration is studied. The role of the control is played by the high thermal conductivity coefficient. For the power-low thermal exchange and the thermal conductivity coefficients the optimality system for considered control problem is obtained. The solvability of control problem is proved under minimal requirements for the smoothness of control; and optimality system is derived with minimal smoothness of the specified functions of boundary value problem.