Displaying similar documents to “Recent results on the Boltzmann equation”

On the interior boundary-value problem for the stationary Povzner equation with hard and soft interactions

Vladislav A. Panferov (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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The Povzner equation is a version of the nonlinear Boltzmann equation, in which the collision operator is mollified in the space variable. The existence of stationary solutions in L 1 is established for a class of stationary boundary-value problems in bounded domains with smooth boundaries, without convexity assumptions. The results are obtained for a general type of collision kernels with angular cutoff. Boundary conditions of the diffuse reflection type, as well as the given incoming...

Diffusive limit for finite velocity Boltzmann kinetic models.

Pierre Louis Lions, Giuseppe Toscani (1997)

Revista Matemática Iberoamericana

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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...