Diffusion approximations of a linear kinetic equation with inelastic scattering: Asymptotic analysis and numerical results

In this work we consider the diffusion approximation of the Boltzmann equat ion in the Lorentz gas limit with inelastic scattering kernel and in the ab sence of fields. We derive the diffusion approximation by using the compres sed Chapman-Enskog method and we evaluate numerically the error of the diff usion approximation for several values of the collision frequency and sever al initial conditions. We also present numerical results showing the releva nt aspects of the time evolution of the distribution function in this physi cal setting.