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Comptes Rendus Mathématique
Volume 341, n° 1
pages 5-10 (juillet 2005)
Doi : 10.1016/j.crma.2005.05.020
Received : 11 April 2005 ;  accepted : 19 May 2005
Convergence to the equilibrium for the Pauli equation without detailed balance condition
Convergence vers lʼequilibre des solutions de lʼéquation de Pauli sans hypothèse dʼéquilibre en détail
 

Naoufel Ben Abdallah a , Miguel Escobedo b , Stéphane Mischler c
a Laboratoire de mathématique pour lʼindustrie et la physique (MIP), université Paul-Sabatier, 118, route de Narbonne, 31062 Toulouse cedex 04, France 
b Departamento de Matemáticas, Universidad del País Vasco, Apartado 644, E48080 Bilbao, Spain 
c Ceremade - UMR 7534, université de Paris IX-Dauphine, place de Lattre de Tassigny, 75775 Paris cedex 16, France 

Abstract

We prove that for  , the homogeneous Boltzmann-Pauli equation, without detailed balance condition on the cross-section, has a unique steady state of total charge . Moreover, we show that the solutions to the Cauchy problem converge to this steady state, as t tends to infinity. To cite this article: N. Ben Abdallah et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).

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

Nous montrons que pour tout  , il existe un unique état stationaire de charge totale pour lʼéquation de Boltzmann-Pauli homogène, sans hypothèse dʼéquilibre en détail sur la section efficace. Nous montrons ensuite la convergence en temps grand vers cet équilibre des solutions du problème de Cauchy. Pour citer cet article : N. Ben Abdallah et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).

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


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