DIFFUSIVE LIMIT FOR FINITE VELOCITY BOLTZMANN KINETIC-MODELS

We investigate, in the diffusive scaling, the limit to the macroscopic description of finite-velocity Boltzmann kinetic models, where the ra te coefficient in front of the collision operator is assumed to be dep endent of the mass density. It is shown that in the limit the flux van ishes, while the evolution of the mass density is governed by a nonlin ear parabolic equation of porous medium type. In the last part of the paper we show that our method adapts to prove the so-called Rosseland approximation in radiative transfer theory.