Classical diffusive limits for the linear Boltzmann equation and study of the Rosseland Approximation in Radiative transfer I

We will review some classical and rigorous diffusion limits for the linear Boltzmann equation as studied in a series of papers by Bardos et al. (1985, 2013), both by using Hilbert series expansions and variational (energy) methods. We shall next introduce an example of nonlinear regime (the so-called Radative Transfer equation) for which the methods mentioned above does not allow to obtain a rigorous diffusive limit (Rosseland approximation).