no. 15-16
Partial Differential Equations
On the Boyd–Kadomtsev system for the three-wave coupling problem
[Sur le système de Boyd–Kadomtsev pour le problème de couplage à trois ondes]

Présenté par : Pierre-Louis Lions

Sentis, Rémi1
1 CEA, DAM, DIF Bruyères, 91297 Arpajon, France
Comptes Rendus. Mathématique, Tome 347 (2009) no. 15-16, pp. 933-938.

Le système de couplage à trois ondes est très utilisé en physique des plasmas, particulierement pour les simulations des instabilités Brillouin. On étudie ici le système avec une vitesse de la lumière infinie ; on montre qu'il est bien posé. Une méthode de discrétisation implicite est proposée (extensible au cas de la vitesse de la lumière finie).

The three-wave coupling system is widely used in plasma physics, specially for the Brillouin instability simulations. We study here a related system obtained with an infinite speed of light. After showing that it is well posed, we propose a numerical method which is based on an implicit time discretization. This method is illustrated on test cases and an extension to the problem with finite speed of light is proposed.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.05.013
Sentis, Rémi 1

1 CEA, DAM, DIF Bruyères, 91297 Arpajon, France 
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Sentis, Rémi. On the Boyd–Kadomtsev system for the three-wave coupling problem. Comptes Rendus. Mathématique, Tome 347 (2009) no. 15-16, pp. 933-938. doi : 10.1016/j.crma.2009.05.013. http://www.numdam.org/articles/10.1016/j.crma.2009.05.013/

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