Optimal control of thermal convection

A problem of optimal control of distributed and boundary thermal sources for a stationary model of natural thermal convection of a high-viscosity inhomogeneous incompressible fluid in the Boussinesq approximation is investigated. Some conditions of solvability of the problem are given, necessary and sufficient conditions of optimality are specified. For the special case of a quality functional conditions of optimality and corresponding adjoint problem defining gradient of the functional are written. Procedure of numerical finding of optimal control based on gradient methods is described. Results of numerical experiments are presented.