Diffusive limit for finite velocity Boltzmann kinetic models.

Lions, Pierre Louis, and Toscani, Giuseppe. "Diffusive limit for finite velocity Boltzmann kinetic models.." Revista Matemática Iberoamericana 13.3 (1997): 473-513. <http://eudml.org/doc/39532>.

@article{Lions1997,
abstract = {We investigate, in the diffusive scaling, the limit to the macroscopic description of finite-velocity Boltzmann kinetic models, where the rate coefficient in front of the collision operator is assumed to be dependent of the mass density. It is shown that in the limit the flux vanishes, while the evolution of the mass density is governed by a nonlinear parabolic equation of porous medium type. In the last part of the paper we show that our method adapts to prove the so-called Rosseland approximation in radiative transfer theory.},
author = {Lions, Pierre Louis, Toscani, Giuseppe},
journal = {Revista Matemática Iberoamericana},
keywords = {Dinámica de fluidos; Ecuaciones diferenciales en derivadas parciales; Modelos cinéticos; Límite superior; Gases; Proceso de difusión; Finitud; Estudio matemático; Boltzmann models; diffusive limit; macroscopic description; a priori estimate; flux; radiative transfer},
language = {eng},
number = {3},
pages = {473-513},
title = {Diffusive limit for finite velocity Boltzmann kinetic models.},
url = {http://eudml.org/doc/39532},
volume = {13},
year = {1997},
}

TY - JOUR
AU - Lions, Pierre Louis
AU - Toscani, Giuseppe
TI - Diffusive limit for finite velocity Boltzmann kinetic models.
JO - Revista Matemática Iberoamericana
PY - 1997
VL - 13
IS - 3
SP - 473
EP - 513
AB - We investigate, in the diffusive scaling, the limit to the macroscopic description of finite-velocity Boltzmann kinetic models, where the rate coefficient in front of the collision operator is assumed to be dependent of the mass density. It is shown that in the limit the flux vanishes, while the evolution of the mass density is governed by a nonlinear parabolic equation of porous medium type. In the last part of the paper we show that our method adapts to prove the so-called Rosseland approximation in radiative transfer theory.
LA - eng
KW - Dinámica de fluidos; Ecuaciones diferenciales en derivadas parciales; Modelos cinéticos; Límite superior; Gases; Proceso de difusión; Finitud; Estudio matemático; Boltzmann models; diffusive limit; macroscopic description; a priori estimate; flux; radiative transfer
UR - http://eudml.org/doc/39532
ER -