[Convergence vers l'equilibre des solutions de l'équation de Pauli sans hypothèse d'équilibre en détail]
Nous montrons que pour tout , 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 , 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.
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@article{CRMATH_2005__341_1_5_0,
author = {Ben Abdallah, Naoufel and Escobedo, Miguel and Mischler, St\'ephane},
title = {Convergence to the equilibrium for the {Pauli} equation without detailed balance condition},
journal = {Comptes Rendus. Math\'ematique},
pages = {5--10},
publisher = {Elsevier},
volume = {341},
number = {1},
year = {2005},
doi = {10.1016/j.crma.2005.05.020},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2005.05.020/}
}
TY - JOUR AU - Ben Abdallah, Naoufel AU - Escobedo, Miguel AU - Mischler, Stéphane TI - Convergence to the equilibrium for the Pauli equation without detailed balance condition JO - Comptes Rendus. Mathématique PY - 2005 SP - 5 EP - 10 VL - 341 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2005.05.020/ DO - 10.1016/j.crma.2005.05.020 LA - en ID - CRMATH_2005__341_1_5_0 ER -
%0 Journal Article %A Ben Abdallah, Naoufel %A Escobedo, Miguel %A Mischler, Stéphane %T Convergence to the equilibrium for the Pauli equation without detailed balance condition %J Comptes Rendus. Mathématique %D 2005 %P 5-10 %V 341 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2005.05.020/ %R 10.1016/j.crma.2005.05.020 %G en %F CRMATH_2005__341_1_5_0
Ben Abdallah, Naoufel; Escobedo, Miguel; Mischler, Stéphane. Convergence to the equilibrium for the Pauli equation without detailed balance condition. Comptes Rendus. Mathématique, Tome 341 (2005) no. 1, pp. 5-10. doi : 10.1016/j.crma.2005.05.020. http://www.numdam.org/articles/10.1016/j.crma.2005.05.020/
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