Displaying similar documents to “The Boltzmann-Enskog equation with large data; wellposedness and regularity”

On the one-dimensional Boltzmann equation for granular flows

Dario Benedetto, Mario Pulvirenti (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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

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...

Recent results on the Boltzmann equation

Carlo Cercignani (1996)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In the last few years the theory of the nonlinear Boltzmann equation has witnessed a veritable turrent of contributions, spurred by the basic result of DiPerna and Lions. Here we wish to survey these results with particular attention to some recent developments.

Kinetic and hydrodynamic equations for granular media

Mario Pulvirenti (1999)

Journées équations aux dérivées partielles

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In this lecture i present some open mathematical problems concerning some PDE arising in the study of one-dimensional models for granular media.