Boundary value and extremal problems for the nonlinear convection–diffusion–reaction equation

We study the boundary value and optimal control problems for stationary nonlinear convection-diffusion-reaction equation, wherein reaction coefficient depends on concentration of substance. The general form of nonlinear reaction coefficient’s dependence on concentration of substance is offered. Solvability of the boundary value and control problems for convection-diffusion-reaction equation is proved. Nonlocal optimality system for the quadratic nonlinearity is obtained, and local uniqueness of extremal problem’s solution for a particular cost functional is proved with the help of optimality system.