On the stability of solutions to coefficient inverse extreme problems for the stationary convection-diffusion equation

We study the coefficient inverse problem for the extreme stationary convection-diffusion, considered in a bounded domain with mixed boundary conditions on the boundary. The role of control is played by the velocity vector of the medium and the functions involved in the boundary conditions for the temperature. The solvability of extremal problems is proved for arbitrary weak lower semicontinuous quality functional as well as for specific quality functionals. On the basis of the analysis of the optimality system, we establish sufficient conditions on the initial data that guarantee the uniqueness and stability of optimal solutions under small perturbations of the quality functional as well as of one of the functions outside the initial boundary value problem.