Asymptotic Analysis of Abstract Linear Kinetic Equations

In this paper we provide a theory of the asymptotic expansion for an abstract kinetic equation. We show that the modified Chapman–Enskog procedure, introduced in [19], gives the error of order of ε², uniformly in time, on the second level of approximation and in particular that the zeroth moment of the solution (the spatial density of particles) can be approximated by the solution of the diffusion-type equation with the same accuracy. The theory is applied to several types of kinetic equations with the Fokker–Planck collision operator.