Stability of solutions of control problems for the convection–diffusion–reaction equation with a strong nonlinearity

Abstract

We consider a boundary control problem for the stationary convection–diffusion–reaction equation in which the reaction constant depends on the concentration of matter in such a way that the equation has a fifth-order nonlinearity. We prove the solvability of the boundary value problem and an extremal problem, derive an optimality system, and analyze it to derive estimates for the local stability of the solution of the extremal problem under small perturbations of both the performance functional and one of the given functions.