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

We study extremal problems of boundary control for stationary heat convection equations with Dirichlet boundary conditions on velocity and temperature. As the cost functional we choose the mean square integral deviation of the required temperature field from a given temperature field measured in some part of the flow region. The controls are functions appearing in the Dirichlet conditions on velocity and temperature. We prove the stability of solutions to these problems with respect to certain perturbations of both the quality functional and one of the known functions appearing in the original equations of the model. © 2011 Pleiades Publishing, Ltd.