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IMA Journal of Applied Mathematics Advance Access originally published online on March 3, 2008
IMA Journal of Applied Mathematics 2008 73(3):539-555; doi:10.1093/imamat/hxn004
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© The Author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Homogenization of the 1D Vlasov–Maxwell equations

M. Bostan{dagger}

Laboratoire de Mathématiques de Besançon, UMR CNRS 6623, Université de Franche-Comté, 16 route de Gray, 25030 Besançon Cedex, France

{dagger} E-mail: mbostan{at}univ-fcomte.fr

Received on December 15, 2006; Accepted on January 23, 2008

In this paper, we investigate the homogenization of the 1D Vlasov–Maxwell system. We indicate the rate of convergence towards the limit solution. In the non-relativistic case, we compute explicitly the limit solution. The theoretical results are illustrated by some numerical simulations.

Keywords: Vlasov–Maxwell equations; homogenization; mild solutions.


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