The problem of radiative heat transfer without boundary conditions for the intensity of radiation

The stationary problem of radiation-diffusion heat transfer in three-\linebreak dimensional domain within the $P_1$ - approximations of the radiation transfer equation is considered. The boundary conditions for the intensity of radiation are not specified, but there is an additional boundary condition for the temperature field. The non-local solvability of the problem is established and it is shown that the set of solutions is homeomorphic to a finite-dimensional compact. Submitted condition uniqueness of the solution. The conditions for the uniqueness of the solution are presented.