Asymptotic analysis for a particle transport problem in a moving medium

In this paper we discuss the derivation of the diffusion theoryfor a linear particle transport in a moving gas. We performthe asymptotic analysis for a one-dimensional linear BGK modelproblem with a shifting Maxwellian which describes the timeevolution of the spatially dependent electron distribution functionin a moving weakly ionized host medium. The modified (compressed)Chapman-Enskog expansion procedure is applied to find the asymptoticsolution for small mean free path , showing that the differencebetween the exact and asymptotic solutions is of order ², uniformlyin time for arbitrary initial data.