Optimal Control Problem for 3D Mass Transfer Model With Concentration‐Dependent Coefficients: Analysis of Properties of Steady Solutions

We study an optimal multiplicative control problem for a 3D stationary mass transfer model with concentration‐dependent coefficients. For the extremum problem under consideration, we derive the optimality system, which has the meaning of necessary conditions for an extremum of the first order. Sufficient conditions for the regularity or non‐degeneracy of this system are also obtained. Based on the analysis of the optimality system, the bang‐bang principle is established for distributed control in one of the extreme problems. This property predetermines the behavior of the optimal control, indicating that it can only “switch” between the boundary points in the set of controls, and therefore, is also called the relay property.