- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:43
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
13
1997
3
Diffusive limit for finite velocity Boltzmann kinetic models
Pierre-Louis
Lions
Univ de Paris IX Dauphine, PARIS CEDEX 05, FRANCE
Giuseppe
Toscani
Università di Pavia, PAVIA, ITALY
We investigate in the diff usive scaling the limit to the macroscopic description of fi nite- velocity Boltzmann kinetic models, where the rate coeffi cient in front of the collision operator is assumed to be dependent of the mass density. It is shown that in the limit the fl ux 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 .
General
473
513
10.4171/RMI/228
http://www.ems-ph.org/doi/10.4171/RMI/228