Theoretical analysis of boundary control extremal problems for Maxwell's equations

Under study are the extremal problems of multiplicative boundary control for timeharmonic Maxwell's equations considered with the impedance boundary condition for the electric field. The solvability of the original extremal problem is proved. Some sufficient conditions are derived on the original data which guarantee the stability of solutions to concrete extremal problems with respect to certain perturbations of both the quality functional and one of the known functions that has the meaning of the density of the electric current.