Displaying similar documents to “Pointwise convergence of Boltzmann solutions for grazing collisions in a Maxwell gas via a probabilitistic interpretation”

The Boltzmann Equation: Mathematics and Applications

Carlo Cercignani (2007)

Bollettino dell'Unione Matematica Italiana

Similarity:

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...

A Langevin Description for Driven Granular Gases

P. Maynar, M. I. García de Soria (2011)

Mathematical Modelling of Natural Phenomena

Similarity:

The study of the fluctuations in the steady state of a heated granular system is reviewed. A Boltzmann-Langevin description can be built requiring consistency with the equations for the one- and two-particle correlation functions. From the Boltzmann-Langevin equation, Langevin equations for the total energy and the transverse velocity field are derived. The existence of a fluctuation-dissipation relation for the transverse velocity field...

Pointwise convergence of Boltzmann solutions for grazing collisions in a Maxwell gas via a probabilitistic interpretation

Hélène Guérin (2004)

ESAIM: Probability and Statistics

Similarity:

Using probabilistic tools, this work states a pointwise convergence of function solutions of the 2-dimensional Boltzmann equation to the function solution of the Landau equation for Maxwellian molecules when the collisions become grazing. To this aim, we use the results of Fournier (2000) on the Malliavin calculus for the Boltzmann equation. Moreover, using the particle system introduced by Guérin and Méléard (2003), some simulations of the solution of the Landau equation will be given....

Stochastic approximations of the solution of a full Boltzmann equation with small initial data

Sylvie Meleard (2010)

ESAIM: Probability and Statistics

Similarity:

This paper gives an approximation of the solution of the Boltzmann equation by stochastic interacting particle systems in a case of cut-off collision operator and small initial data. In this case, following the ideas of Mischler and Perthame, we prove the existence and uniqueness of the solution of this equation and also the existence and uniqueness of the solution of the associated nonlinear martingale problem. 
Then, we first delocalize the interaction by considering a mollified...

Conservative forms of Boltzmann's collision operator: Landau revisited

Cédric Villani (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

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.

Kinetic and hydrodynamic equations for granular media

Mario Pulvirenti (1999)

Journées équations aux dérivées partielles

Similarity:

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