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.