Optimal control of the radiation heat exchange equations for multi-component media

Abstract

An analysis of optimal control problems for nonlinear elliptic equations modeling complex heat transfer with Fresnel conjugation conditions on the discontinuity surfaces of the refractive index is presented. Conditions for the solvability of extremal problems and the nondegeneracy of the optimality system are obtained. For the control problem with boundary observation, the bang-bang property is set.