Comptes Rendus
no. 1
Partial Differential Equations
Convergence to the equilibrium for the Pauli equation without detailed balance condition
[Convergence vers l'equilibre des solutions de l'équation de Pauli sans hypothèse d'équilibre en détail]

Présenté par : Pierre-Louis Lions

Naoufel Ben Abdallah1 ; Miguel Escobedo2 ; Stéphane Mischler3
1 Laboratoire de mathématique pour l'industrie et la physique (MIP), université Paul-Sabatier, 118, route de Narbonne, 31062 Toulouse cedex 04, France
2 Departamento de Matemáticas, Universidad del País Vasco, Apartado 644, E48080 Bilbao, Spain
3 Ceremade – UMR 7534, université de Paris IX–Dauphine, place de Lattre de Tassigny, 75775 Paris cedex 16, France
Comptes Rendus. Mathématique, Volume 341 (2005) no. 1, pp. 5-10.

Nous montrons que pour tout ρ∈(0,1), il existe un unique état stationaire de charge totale ρ pour l'équation de Boltzmann–Pauli homogène, sans hypothèse d'équilibre en détail sur la section efficace. Nous montrons ensuite la convergence en temps grand vers cet équilibre des solutions du problème de Cauchy.

We prove that for ρ∈(0,1), the homogeneous Boltzmann–Pauli equation, without detailed balance condition on the cross-section, has a unique steady state of total charge ρ. Moreover, we show that the solutions to the Cauchy problem converge to this steady state, as t tends to infinity.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.05.020
Naoufel Ben Abdallah 1 ; Miguel Escobedo 2 ; Stéphane Mischler 3

1 Laboratoire de mathématique pour l'industrie et la physique (MIP), université Paul-Sabatier, 118, route de Narbonne, 31062 Toulouse cedex 04, France
2 Departamento de Matemáticas, Universidad del País Vasco, Apartado 644, E48080 Bilbao, Spain
3 Ceremade – UMR 7534, université de Paris IX–Dauphine, place de Lattre de Tassigny, 75775 Paris cedex 16, France 
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Naoufel Ben Abdallah; Miguel Escobedo; Stéphane Mischler. Convergence to the equilibrium for the Pauli equation without detailed balance condition. Comptes Rendus. Mathématique, Volume 341 (2005) no. 1, pp. 5-10. doi : 10.1016/j.crma.2005.05.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.05.020/

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