Comptes Rendus
no. 9-10
Partial Differential Equations/Mathematical Physics
Analytic solutions to a strongly nonlinear Vlasov equation
[Solutions analytiques à une équation de type Vlasov fortement non linéaire]

Présenté par : the Editorial Board

Pierre-Emmanuel Jabin1 ; A. Nouri2
1 Laboratoire Dieudonné, University of Nice-Sophia Antipolis, parc Valrose, 06000 Nice, France
2 Aix-Marseille University, France
Comptes Rendus. Mathématique, Volume 349 (2011) no. 9-10, pp. 541-546.

Nous démontrons lʼexistence en temps petit de solution analytique à une équation de type Vlasov. Le modèle considéré est mono-dimensionnel mais le terme de force correspondant fait intervenir une dérivée complète de la densité macroscopique. Ceci rend la question de lʼexistence de solution particulièrement délicate.

We prove the existence for short times of analytic solutions to a Vlasov type equation. The corresponding model is one-dimensional but uses a quite singular force term which involves a full derivative in x of the macroscopic density, making the existence of solutions a difficult question.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.03.024
Pierre-Emmanuel Jabin 1 ; A. Nouri 2

1 Laboratoire Dieudonné, University of Nice-Sophia Antipolis, parc Valrose, 06000 Nice, France
2 Aix-Marseille University, France 
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Pierre-Emmanuel Jabin; A. Nouri. Analytic solutions to a strongly nonlinear Vlasov equation. Comptes Rendus. Mathématique, Volume 349 (2011) no. 9-10, pp. 541-546. doi : 10.1016/j.crma.2011.03.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.03.024/

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