Weak solutions of the Vlasov–Poisson initial boundary value problem

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.