Analysis of Control Problems for Stationary Magnetohydrodynamics Equations under the Mixed Boundary Conditions for a Magnetic Field

The optimal control problems for stationary magnetohydrodynamic equations under the inhomogeneous mixed boundary conditions a magnetic field and Dirichlet condition velocity are considered. role of controls in study is played by normal tangential components given on different parts exterior current density. Quadratic tracking-type functionals velocity, or pressure taken as cost functionals. global solvability consideration proved, an optimality system derived and, based its analysis, mathematical apparatus studying local uniqueness stability solutions developed. On basis developed apparatus, specific estimates established.