ANALYSIS, OPTIMAL CONTROL, AND SIMULATION OF CONDUCTIVE-RADIATIVE HEAT TRANSFER

This article surveys recent results regarding the existence of weaksolutions to quasilinear partial differential equations(PDE)couplednonlocally by the integral operator of the radiosity equation, modeling conductive-radiative heat transfer. Both the stationary and the transient case are considered. For the stationary case, an optimal control problem with control constraints is presented withfirst-order necessary optimality conditions, where recent results on the solution theory of the linearized state equation allow to close a previous gap.Afinite volume scheme for the discretization of the stationary system is described and, based on this scheme, a numerical computation of the temperaturefield(solution of the state equation)is shown as well as the numerical solution to a realistic control problem in the context of industrial applications in crystal growth.