The stability of solutions to extremal problems of boundary control for stationary heat convection equations

We study the extremal problems of boundary control for the stationary heat convection equations with Dirichlet boundary conditions on the velocity and temperature. As cost functionals we choose the mean square deviation of the required temperature field from the temperature field measured in some part of the flow region. The controls are functions involved in the Dirichlet conditions. We prove the stability of solutions under certain perturbations of both the quality functional and one of the known functions involved in the original equations of the model.