The Diffusion Approximation for the Linear Boltzmann Equation with Vanishing Scattering Coefficient

Claude Bardos (1) , Etienne Bernard (2) , François Golse (3) , Remi Sentis (1)

1 LJLL - Laboratoire Jacques-Louis Lions
2 LAREG - LAboratoire de REcherche en Géodésie [Paris]
3 CMLS - Centre de Mathématiques Laurent Schwartz

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.

Mots clés: Linear Boltzmann equation; Diffusion approximation; Neutron transport equation; Radiative transfer equation

Domaines: Equations aux dérivées partielles [math.AP]

Claude Bardos, Etienne Bernard, François Golse, Remi Sentis. The Diffusion Approximation for the Linear Boltzmann Equation with Vanishing Scattering Coefficient. Communications in Mathematical Sciences, 2015, 13 (3), pp. 641-671. ⟨10.4310/CMS.2015.v13.n3.a3⟩. ⟨hal-00859228⟩