Characterization of collision kernels

Laurent Desvillettes; Francesco Salvarani

Displaying similar documents to “Characterization of collision kernels”

The Boltzmann Equation: Mathematics and Applications

Carlo Cercignani (2007)

Bollettino dell'Unione Matematica Italiana

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The paper is subdivided into two parts. The first presents a recent result by the author concerning the existence of the solution of the Boltzmann equation for Maxwell molecules, without any cutoff in the collision kernel, when the solution depends on just one variable. At variance with the well-known theorem of DiPerna- Lions, conservation of energy is also shown to hold. The second part will concern rarefied gas dynamics problems, governed by the Boltzmann equation and con- cerning...

Generalization of the Mercer Theorem

Milutin Dostanić (1993)

Publications de l'Institut Mathématique

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On the one-dimensional Boltzmann equation for granular flows

Dario Benedetto, Mario Pulvirenti (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider a Boltzmann equation for inelastic particles on the line and prove existence and uniqueness for the solutions.

On the Landau approximation in plasma physics

R Alexandre, C Villani (2004)

Annales de l'I.H.P. Analyse non linéaire

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Conservative forms of Boltzmann's collision operator: Landau revisited

Cédric Villani (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We show that Boltzmann's collision operator can be written explicitly in divergence and double divergence forms. These conservative formulations may be of interest for both theoretical and numerical purposes. We give an application to the asymptotics of grazing collisions.