Nondegeneracy of optimality conditions in control problems for a radiative–conductive heat transfer model

A boundary control problem for a nonlinear steady-state heat transfer model accounting for heat radiation effects is considered. The problem consists in the minimization of a cost functional by controlling the reflection properties of the boundary. The solvability of the control problem is proven, an optimality system is derived, and the nondegeneracy of optimality conditions is established. The results of numerical simulations are presented.