Boundary Value and Control Problems for Mass Transfer Equations with Variable Coefficients

Boundary value and control problems for nonlinear mass transfer equation are studied in the case when the viscosity and diffusion coefficients depend on the substance's concentration and then the reaction coefficient depends on the substance's concentration and also depends on spatial variables. For the substance's concentration, as a component of a weak solution of a boundary value problem, a maximum principle has been established. The local existence of a strong solution of the boundary value problem for the reaction coefficients, which generalizes power-law dependences of the substance's concentration, is proven. The uniqueness of a small solution according to the corresponding norms of a strong solution is proven. The solvability of the control problem is proven for weak solutions of the boundary value problem.