Finite speed propagation of the solutions for the relativistic Vlasov-Maxwell system
نویسنده
چکیده
In this report we investigate the continuous dependence with respect to the initial data of the solutions for the 1D and 1.5D relativistic Vlasov-Maxwell system. More precisely we prove that these solutions propagate with finite speed. We formulate our results in the framework of mild solutions, i.e., the particle densities are solutions by characteristics and the electro-magnetic fields are Lipschitz continuous functions. Key-words: Vlasov-Maxwell equations, mild solutions, characteristics, finite speed propagation ∗ Laboratoire de Mathématiques de Besançon, UMR CNRS 6623, Université de Franche-Comté, 16 route de Gray, 25030 Besançon Cedex France et INRIA Lorraine, projet CALVI. E-mail : [email protected] [email protected] in ria -0 01 20 71 9, v er si on 4 20 F eb 2 00 8 Propagation à vitesse finie des solutions des équations de Vlasov-Maxwell Résumé : Dans ce rapport nous étudions la dépendance continue des solutions des équations relativistes de Vlasov-Maxwell. Plus précisément on montre la propagation à vitesse finie, la vitesse de propagation étant au plus égale à la vitesse de la lumière. Mots-clés : Equations relativistes de Vlasov-Maxwell, solutions par caractéristiques, vitesse finie de propagation in ria -0 01 20 71 9, v er si on 4 20 F eb 2 00 8 Finite speed propagation for the Vlasov-Maxwell system 3
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