Optimal Multiplicative Control in the Reaction–Diffusion–Convection Model With Concentration‐Dependent Coefficients

The solvability of a multiplicative control problem on weak solutions of the Dirichlet boundary value problem for the reaction–diffusion–convection equation with concentration‐dependent coefficients is proved. For an extremum problem with specific diffusion and reaction coefficients, suitable optimality systems are obtained on strong solutions. For these coefficients, a method for proving the existence of strong solutions to the corresponding boundary value problem has been developed and applied. Based on the analysis of the optimality system, the bang‐bang principle for optimal controls is established. Moreover, an optimal multiplicative feedback control problem is considered. It is shown that there exist weak solutions that minimize a given cost functional. To establish this result, we suggest a non‐standard approach, which is based on the interpretation of a control system as some operator inclusion with a continuous monotone‐type mapping and a compact upper semicontinuous multivalued mapping having aspheric image sets.