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Local Existence and Uniqueness of a Mild Solution to the One Dimensional Vlasov-Poisson System with an Initial Condition of Bounded Variation

Simon Labrunie 1, 2 Sandrine Marchal 1, 2 Jean Rodolphe Roche 1, 2
1 CALVI - Scientific computation and visualization
IRMA - Institut de Recherche Mathématique Avancée, LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection, Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine
Abstract : We propose a result of local existence and uniqueness of a mild solution to the one-dimensional Vlasov-Poisson system. We establish the result for an initial condition lying in the Sobolev space of integrable functions with integrable derivatives, then we extend it to initial conditions lying in the space of functions of bounded variation, without any assumption of continuity, boundedness or compact support.
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https://hal.inria.fr/inria-00389829
Contributor : Sandrine Marchal <>
Submitted on : Friday, May 29, 2009 - 5:08:04 PM
Last modification on : Tuesday, March 2, 2021 - 5:12:05 PM
Long-term archiving on: : Monday, October 15, 2012 - 11:26:58 AM

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  • HAL Id : inria-00389829, version 1

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Simon Labrunie, Sandrine Marchal, Jean Rodolphe Roche. Local Existence and Uniqueness of a Mild Solution to the One Dimensional Vlasov-Poisson System with an Initial Condition of Bounded Variation. [Research Report] RR-6946, INRIA. 2009, pp.14. ⟨inria-00389829⟩

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