Asymptotic analysis for a particle transport problem in a moving medium

In this paper we discuss the derivation of the diffusion theory for a linear particle transport in a moving gas. We perform the asymptotic analysis for a one-dimensional linear BGK model problem with a shifting Maxwellian which describes the time evolution of the spatially dependent electron distribution function in a moving weakly ionized host medium. The modified (compressed) Chapman-Enskog expansion procedure is applied to find the asymptotic solution for small mean free path ∈, showing that the difference between the exact and asymptotic solutions is of order ∈2, uniformly in time for arbitrary initial data.