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Diffusive limit for finite velocity Boltzmann kinetic models

Lions, Pierre-Louis; Toscani, Giuseppe (1997), Diffusive limit for finite velocity Boltzmann kinetic models, Revista Matematica Iberoamericana, 13, 3, p. 473-513

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Type
Article accepté pour publication ou publié
Date
1997
Nom de la revue
Revista Matematica Iberoamericana
Volume
13
Numéro
3
Éditeur
Real Sociedad Matemática Española
Pages
473-513
Métadonnées
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Auteur(s)
Lions, Pierre-Louis
Toscani, Giuseppe
Résumé (EN)
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.
Mots-clés
Rosseland approximation; radiative transfer theory; nonlinear parabolic equations; Boltzmann kinetic models