Inverse problem with finite overdetermination for steady-state equations of radiative heat exchange

An inverse problem for a system of semilinear elliptic equations modeling simultaneously conductive and radiative heat transfer is under consideration. The problem consists in finding the right-hand side of the heat transfer equation, in the form of linear combination of given functionals, on the base of prescribed values of these functionals on the solution. The solvability of the problem is proven without any smallness assumptions. It is shown that the set of solutions is homeomorphic to a finite-dimensional compact set, and conditions of uniqueness of solutions are found.