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Periodic Solutions of the Vlasov-Poisson System with Boundary Conditions

Mihai Bostan 1 Frédéric Poupaud
1 CAIMAN - Scientific computing, modeling and numerical analysis
CRISAM - Inria Sophia Antipolis - Méditerranée , ENPC - École des Ponts ParisTech, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : We study the Vlasov-Poisson system with time periodic boundary conditions. For small data we prove existence of weak periodic solutions in any space dimension. In the one dimensional case the result is stronger: we obtain existence of mild solution and uniqueness of this solution when the data are smooth. It is necessary to impose a non vanishing condition for the incoming velocities in order to control the life-time of particles in the domain.
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Submitted on : Wednesday, May 24, 2006 - 12:02:15 PM
Last modification on : Thursday, April 5, 2018 - 10:24:16 AM
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  • HAL Id : inria-00073166, version 1



Mihai Bostan, Frédéric Poupaud. Periodic Solutions of the Vlasov-Poisson System with Boundary Conditions. RR-3518, INRIA. 1998. ⟨inria-00073166⟩



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