Revista Matemática Iberoamericana

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Volume 13, Issue 3, 1997, pp. 473–513
DOI: 10.4171/RMI/228

Diffusive limit for finite velocity Boltzmann kinetic models

Pierre-Louis Lions[1] and Giuseppe Toscani[2]

(1) CEREMADE, Université de Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775, PARIS CEDEX 05, FRANCE
(2) Dipartimento di Matematica, Università di Pavia, Via Ferrata 1, I-27100, PAVIA, ITALY

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.

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Lions Pierre-Louis, Toscani Giuseppe: Diffusive limit for finite velocity Boltzmann kinetic models. Rev. Mat. Iberoamericana 13 (1997), 473-513. doi: 10.4171/RMI/228