Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Mild solutions for the relativistic Vlasov-Maxwell system for laser-plasma interaction

Author: Mihai Bostan
Journal: Quart. Appl. Math. 65 (2007), 163-187
MSC (2000): Primary 35A05, 35B35; Secondary 82D10
DOI: https://doi.org/10.1090/S0033-569X-07-01047-4
Published electronically: February 12, 2007
MathSciNet review: 2313155
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Abstract: We study a reduced $ 1$D Vlasov-Maxwell system which describes the laser-plasma interaction. The unknowns of this system are the distribution function of charged particles, satisfying a Vlasov equation, the electrostatic field, verifying a Poisson equation and a vector potential term, solving a nonlinear wave equation. The nonlinearity in the wave equation is due to the coupling with the Vlasov equation through the charge density. We prove here the existence and uniqueness of the mild solution (i.e., solution by characteristics) in the relativistic case by using the iteration method.

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Additional Information

Mihai Bostan
Affiliation: Laboratoire de Mathématiques de Besançon, Université de Franche-Comté, 16 route de Gray 25030 Besançon France
Email: mbostan@math.univ-fcomte.fr

DOI: https://doi.org/10.1090/S0033-569X-07-01047-4
Keywords: Kinetic equations, Vlasov-Maxwell system, weak/mild solution, characteristics
Received by editor(s): July 21, 2006
Published electronically: February 12, 2007
Article copyright: © Copyright 2007 Brown University

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