Nous étudions l'existence de solution périodique en temps pour les équations de Vlasov–Maxwell dans un domaine borné tridimensionnel. On suppose que la frontière du domaine est strictement étoilée. Nous donnons également des estimations a priori pour l'énergie cinétique et électromagnétique ainsi que pour les traces normales et tangentielles du champ électromagnétique. La méthode utilisée permet de traiter à la fois les cas classique et relativiste.
We study here the existence of time periodic solution for the Vlasov–Maxwell equations in a three dimensional bounded domain. We assume that the boundary of the domain is strictly star-shaped. We give a priori estimates for the kinetic and electro-magnetic energy, and also for the normal and tangential traces of the electro-magnetic field. This method allows us to treat both classical and relativistic cases.
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@article{CRMATH_2004__339_6_451_0,
author = {Bostan, Mihai},
title = {Solutions p\'eriodiques en temps des \'equations de {Vlasov{\textendash}Maxwell}},
journal = {Comptes Rendus. Math\'ematique},
pages = {451--456},
publisher = {Elsevier},
volume = {339},
number = {6},
year = {2004},
doi = {10.1016/j.crma.2004.07.008},
language = {fr},
url = {http://www.numdam.org/articles/10.1016/j.crma.2004.07.008/}
}
TY - JOUR AU - Bostan, Mihai TI - Solutions périodiques en temps des équations de Vlasov–Maxwell JO - Comptes Rendus. Mathématique PY - 2004 SP - 451 EP - 456 VL - 339 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.07.008/ DO - 10.1016/j.crma.2004.07.008 LA - fr ID - CRMATH_2004__339_6_451_0 ER -
%0 Journal Article %A Bostan, Mihai %T Solutions périodiques en temps des équations de Vlasov–Maxwell %J Comptes Rendus. Mathématique %D 2004 %P 451-456 %V 339 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2004.07.008/ %R 10.1016/j.crma.2004.07.008 %G fr %F CRMATH_2004__339_6_451_0
Bostan, Mihai. Solutions périodiques en temps des équations de Vlasov–Maxwell. Comptes Rendus. Mathématique, Tome 339 (2004) no. 6, pp. 451-456. doi : 10.1016/j.crma.2004.07.008. http://www.numdam.org/articles/10.1016/j.crma.2004.07.008/
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