[Solutions analytiques à une équation de type Vlasov fortement non linéaire]
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.
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@article{CRMATH_2011__349_9-10_541_0,
author = {Jabin, Pierre-Emmanuel and Nouri, A.},
title = {Analytic solutions to a strongly nonlinear {Vlasov} equation},
journal = {Comptes Rendus. Math\'ematique},
pages = {541--546},
publisher = {Elsevier},
volume = {349},
number = {9-10},
year = {2011},
doi = {10.1016/j.crma.2011.03.024},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2011.03.024/}
}
TY - JOUR AU - Jabin, Pierre-Emmanuel AU - Nouri, A. TI - Analytic solutions to a strongly nonlinear Vlasov equation JO - Comptes Rendus. Mathématique PY - 2011 SP - 541 EP - 546 VL - 349 IS - 9-10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2011.03.024/ DO - 10.1016/j.crma.2011.03.024 LA - en ID - CRMATH_2011__349_9-10_541_0 ER -
%0 Journal Article %A Jabin, Pierre-Emmanuel %A Nouri, A. %T Analytic solutions to a strongly nonlinear Vlasov equation %J Comptes Rendus. Mathématique %D 2011 %P 541-546 %V 349 %N 9-10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2011.03.024/ %R 10.1016/j.crma.2011.03.024 %G en %F CRMATH_2011__349_9-10_541_0
Jabin, Pierre-Emmanuel; Nouri, A. Analytic solutions to a strongly nonlinear Vlasov equation. Comptes Rendus. Mathématique, Tome 349 (2011) no. 9-10, pp. 541-546. doi : 10.1016/j.crma.2011.03.024. http://www.numdam.org/articles/10.1016/j.crma.2011.03.024/
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