Lions, Pierre Louis; Toscani, Giuseppe Diffusive limit for finite velocity Boltzmann kinetic models. (English) Zbl 0896.35109 Rev. Mat. Iberoam. 13, No. 3, 473-513 (1997). The authors investigate, in the diffusive scaling, the limit to the macroscopic equations of finite-velocity Boltzmann kinetic models, when the rate coefficient in front of the collision operator is assumed to be dependent of the mass density. One proves that the flux converges to zero and the limit mass density is the weak solution to the Cauchy problem for the slow diffusion equation. Finally, one states without proof various extensions and variants of the obtained results. In particular, one makes contact with the so-called Rosseland approximation in radiative transfer theory. Reviewer: V.A.Sava (Iaşi) Cited in 72 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics 76R50 Diffusion Keywords:Boltzmann models; diffusive limit; macroscopic description; a priori estimate; flux; radiative transfer PDFBibTeX XMLCite \textit{P. L. Lions} and \textit{G. Toscani}, Rev. Mat. Iberoam. 13, No. 3, 473--513 (1997; Zbl 0896.35109) Full Text: DOI EuDML