Problems on control for a steady-state magnetic-hydrodynamic model of a viscous heat-conducting fluid under mixed boundary conditions

Abstract

The control problems for steady-state equations of magnetic hydrodynamics (MHD) for a viscous heat-conducting fluid considered under mixed boundary conditions for the magnetic field and temperature are investigated. Their solvability is proved, the optimality systems describing the necessary conditions of an extremum are derived, and the theorems of local uniqueness and stability of the optimum solutions for explicit quality functionals are formulated.