Optimal Control of Complex Heat Transfer Equations with Cauchy Boundary Conditions

The paper presents an analysis of an optimal control problem for a stationary diffusion model of complex heat transfer, including a $${{P}_{1}}$$ -approximation of the thermal radiative transfer equation. A formulation is considered in which the boundary temperature and its normal derivative are known, while the boundary conditions for the radiation intensity are not specified. The solvability of the control problem is established, and necessary optimality conditions are obtained. A sufficient condition for the uniqueness of a solution of an optimal control problem is presented.