Theoretical analysis of an optimal control problem of conductive-convective-radiative heat transfer

The problem of optimal heat removal from a three-dimensional domain is considered. The specific of the study consist in accounting for the radiative heat transfer. The so-called P1 approximation of the radiative heat transfer equation is used, which reduces the model to a nonlinear elliptic system. A problem of optimal boundary control of this system is considered. The solvability of the control problem is proved, and necessary optimality conditions of first order are derived. Examples of non-singularity of these conditions are given.