  We study the diffusive limit approximation for a nonlinear radiative heat
transfer system that arises in the modeling of glass cooling, greenhouse
effects and in astrophysics. The model is considered with the reflective
radiative boundary conditions for the radiative intensity, and periodic,
Dirichlet and Robin boundary conditions for the temperature. The global
existence of weak solutions for this system is given by using a Galerkin method
with a careful treatment of the boundary conditions. Using the compactness
method, averaging lemma and Young measure theory, we prove our main result that
the weak solution converges to a nonlinear diffusion model in the diffusive
limit. Moreover, under more regularity conditions on the limit system, the
diffusive limit is also analyzed by using a relative entropy method. In
particular, we get a rate of convergence. The initial and boundary conditions
are assumed to be well-prepared in the sense that no initial and boundary layer
exist.
