The Diffusion Approximation for the Linear Boltzmann Equation with Vanishing Scattering Coefficient
Analysis of PDEs
2015-03-23 v1 Mathematical Physics
math.MP
Abstract
The present paper discusses the diffusion approximation of the linear Boltzmann equation in cases where the collision frequency is not uniformly large in the spatial domain. Our results apply for instance to the case of radiative transfer in a composite medium with optically thin inclusions in an optically thick background medium. The equation governing the evolution of the approximate particle density coincides with the limit of the diffusion equation with infinite diffusion coefficient in the optically thin inclusions.
Cite
@article{arxiv.1309.1774,
title = {The Diffusion Approximation for the Linear Boltzmann Equation with Vanishing Scattering Coefficient},
author = {Claude Bardos and Etienne Bernard and François Golse and Rémi Sentis},
journal= {arXiv preprint arXiv:1309.1774},
year = {2015}
}
Comments
30 pages