DIFFUSION LIMIT FOR THE LINEAR BOLTZMANN-EQUATION OF THE NEUTRON-TRANSPORT THEORY

In this paper we present the asymptotic analysis of the linear Boltzmann equation for neutrons with a small positive parameter epsilon related to the mean free path, based upon the Chapman-Enskog procedure of the kinetic theory. We prove that if proper initial conditions derived by considering initial layer solutions are used, the diffusion equation gives the uniform approximation to the neutron density function with the O(epsilon2) accuracy.