Communications in Mathematical Sciences

Volume 13 (2015)

Number 3

Special Issue in Honor of George Papanicolaou’s 70th Birthday

Guest Editors: Liliana Borcea, Jean-Pierre Fouque, Shi Jin, Lenya Ryzhik, and Jack Xin

The diffusion approximation for the linear Boltzmann equation with vanishing scattering coefficient

Pages: 641 – 671



Claude Bardos (Laboratoire Jacques-Louis Lions, Paris, France)

Etienne Bernard (Institut Géographique National, Laboratoire de Recherche en Géodésie, Université Paris Diderot, Paris, France)

François Golse (Ecole Polytechnique, Centre de Mathématiques Laurent Schwartz, Palaiseau, France)

Rémi Sentis (Laboratoire Jacques-Louis Lions, Paris, France)


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.


linear Boltzmann equation, diffusion approximation, neutron transport equation, radiative transfer equation

2010 Mathematics Subject Classification

45M05, 82C70, 85A25

Published 3 March 2015