Analysis for Optimal Boundary Control for a Three-dimensional Reaction-diffusion System

This paper is concerned with optimal boundary control of an instationary reaction-diffusion system in three spatial dimensions. This problem involves a coupled nonlinear system of parabolic differential equations with bilateral as well as integral control constraints. The integral constraint is included in the cost by a penalty term whereas the bilateral control constraints are handled explicitly. Firstand second-order conditions for the optimization problem, which involves bilateral and integral control constraints, are analyzed. A primal-dual active set strategy is utilized to compute optimal solutions numerically. The algorithm is compared to a semi-smooth Newton method.