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Diffusion limit for the linear boltzmann equation of the neutron transport theory
Author(s) -
Banasiak J.,
Mika J. R.
Publication year - 1994
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670171306
Subject(s) - boltzmann equation , mathematics , limit (mathematics) , neutron transport , mean free path , diffusion , convection–diffusion equation , diffusion equation , mathematical analysis , lattice boltzmann methods , kinetic theory , neutron , boltzmann constant , heavy traffic approximation , statistical physics , physics , quantum mechanics , thermodynamics , scattering , economy , economics , service (business) , statistics
In this paper we present the asymptotic analysis of the linear Boltzmann equation for neutrons with a small positive parameter ϵ 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 (ϵ 2 ) accuracy.