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Comptes Rendus Mathématique
Volume 335, n° 4
pages 337-340 (2002)
Doi : S1631-073X(02)02495-0
Received : 30 June 2002 ;  accepted : 1 July 2002
L1 contraction property for a Boltzmann equation with Pauli statistics
Propriété de contraction L1 pour l'équation de Boltzmann avec la statistique de Pauli
 

Antoine Mellet a , Benoı̂t Perthame b
a Laboratoire mathématiques pour l'industrie et la physique, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse cedex 04, France 
b Département de mathématiques et applications, UMR 8553, École normale supérieure, 45, rue d'Ulm, 75230 Paris cedex 05, France 

Note presented by Phillipe G. Ciarlet

Abstract

We establish a L1 contraction property for solutions to the Boltzmann equation when collisions are taken into account through the Pauli operator. The Pauli operator is a non-linear integral operator, that we consider here in full generality, without assuming relations such as the detailed balance principle. It takes into account the Pauli exclusion principle and appears especially to describe the flow of electrons and holes in some semi-conductor devices. To cite this article: A. Mellet, B. Perthame, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 337-340.

The full text of this article is available in PDF format.
Résumé

Nous établissons une propriété de contraction L1 pour les solutions de l'équation de Boltzmann lorsque les collisions sont décrites par l'opérateur de Pauli. L'opérateur de Pauli est un opérateur intégral non-linéaire, qui prend en compte le principe d'exclusion de Pauli et qui est utilisé pour décrire les flots d'électrons et de trous dans certains dispositifs semiconducteurs. On le considère ici sans hypothèse suplémentaire, telle que la relation d'équilibre en détail. Pour citer cet article : A. Mellet, B. Perthame, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 337-340.

The full text of this article is available in PDF format.


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