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Weak solutions of the Vlasov–Poisson initial boundary value problem
Author(s) -
Alexandre Radjesvarane
Publication year - 1993
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670160807
Subject(s) - mathematics , boundary value problem , dirichlet boundary condition , mathematical analysis , homogenization (climate) , laplace transform , poisson's equation , laplace's equation , homogeneous , poisson distribution , initial value problem , discrete poisson equation , vlasov equation , plasma , physics , biodiversity , ecology , statistics , combinatorics , quantum mechanics , biology
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.