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Weak solutions of the Vlasov–Poisson initial boundary value problem

✍ Scribed by Radjesvarane Alexandre

Publisher
John Wiley and Sons
Year
1993
Tongue
English
Weight
1018 KB
Volume
16
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

This paper deals with existence results for a Vlasov‐Poisson system, equipped with an absorbing‐type law for the Vlasov equation and a Dirichlet‐type boundary condition for the Poisson part. Using the ideas of Lions and Perthame [21], we prove the existence of a weak solution having good L^p^ estimates for moment and electric field, by a good control on the higher moments of the initial data. As an application, we establish a homogenization result in the Hilbertian framework for this type of problem in non‐homogeneous media, following the work by Alexandre and Hamdache [2] for general kinetic equations, and Cioranescu and Mural [11] for the Laplace problem.

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