Analysis of inverse extremal problems for the non-linear stationary mass-transfer equations

This work deals with inverse extremal problems for the non-linear stationary mass-transfer equations. The states of system are the velocity, pressure of fluid and concentration of substance. The control problem consists in minimizing one of two cost functionals. Existence of optimal solutions is proved and existence of Lagrange multipliers is verified. The optimality conditions for these problems are derived. Regularity solutions of Lagrange multipliers is studied and sufficient conditions of uniqueness of the inverse extremal problems for the concrete functional are derived.