Optimal Control of Complex Heat Transfer Equations With Cauchy Boundary Conditions

This paper presents an analysis of the optimal control problem for a steady- state diffusion model of complex heat transfer, including the - approximation of the radiative heat transfer equation. A formulation is considered in which the boundary values of the temperature and its normal derivative are known, while the boundary conditions for the radiative intensity are not specified. The solvability of the control problem is established, and the necessary optimality conditions are obtained. A sufficient condition for the uniqueness of a solution to the optimal control problem is presented.