Characterization of collision kernels

Laurent Desvillettes; Francesco Salvarani

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2003)

  • Volume: 37, Issue: 2, page 345-355
  • ISSN: 0764-583X

Abstract

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In this paper we show how abstract physical requirements are enough to characterize the classical collision kernels appearing in kinetic equations. In particular Boltzmann and Landau kernels are derived.

How to cite

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Desvillettes, Laurent, and Salvarani, Francesco. "Characterization of collision kernels." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 37.2 (2003): 345-355. <http://eudml.org/doc/245775>.

@article{Desvillettes2003,
abstract = {In this paper we show how abstract physical requirements are enough to characterize the classical collision kernels appearing in kinetic equations. In particular Boltzmann and Landau kernels are derived.},
author = {Desvillettes, Laurent, Salvarani, Francesco},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Boltzmann; Landau; collision kernels; Boltzmann kernel; Landau kernel},
language = {eng},
number = {2},
pages = {345-355},
publisher = {EDP-Sciences},
title = {Characterization of collision kernels},
url = {http://eudml.org/doc/245775},
volume = {37},
year = {2003},
}

TY - JOUR
AU - Desvillettes, Laurent
AU - Salvarani, Francesco
TI - Characterization of collision kernels
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2003
PB - EDP-Sciences
VL - 37
IS - 2
SP - 345
EP - 355
AB - In this paper we show how abstract physical requirements are enough to characterize the classical collision kernels appearing in kinetic equations. In particular Boltzmann and Landau kernels are derived.
LA - eng
KW - Boltzmann; Landau; collision kernels; Boltzmann kernel; Landau kernel
UR - http://eudml.org/doc/245775
ER -

References

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  7. [7] L. Desvillettes and C. Villani, On the spatially homogeneous Landau equation for hard potentials. Part I: Existence, uniqueness and smoothness. Comm. Partial Differential Equations 25 (2000) 179–259. Zbl0946.35109
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  12. [12] R. Illner and M. Pulvirenti, Global validity of the Boltzmann equation for a two-dimensional rare gas in the vacuum. Comm. Math. Phys. 105 (1986) 189–203. Zbl0609.76083
  13. [13] R. Illner and M. Pulvirenti, Global validity of the Boltzmann equation for two- and three-dimensional rare gas in the vacuum: erratum and improved result. Comm. Math. Phys. 121 (1989) 143–146. Zbl0850.76600
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