Half space problems for frequency dependent transport equations. Application to the Rosseland approximation of the radiative transfer equations

When the mean free path of the photons are small the radiative transfer equation may be approximated by a non linear diffusion equation. In order to find the right boundary condition for this last equation it is necessary to solve a non linear frequency dependent transport equation in a half space. This non linear half space problem is first studied. Afterwards a linearized half space problem is considered and the limit of the solution is calculated using Chandrasekhar's techniques.