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Boundary value problems for the stationary Vlasov-Maxwell system. (English) Zbl 0785.35020

Summary: The Vlasov-Maxwell equations provide a kinetic description of the flow of particles in a self-consistent electromagnetic field. The aim of this paper is to prove the existence of stationary solutions for boundary value problems with arbitrary large data. The main idea consists in using explicit upper solutions for the Vlasov equation that allow to bound the particles concentration and flux. A key point is that the electric field is repulsive. The mathematical analysis is first given for the relativistic Vlasov-Maxwell system. Next, the results are extended to classical mechanics, systems with several species of particles and Boltzmann-Vlasov-Poisson problems.

MSC:

35F30 Boundary value problems for nonlinear first-order PDEs
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
78A35 Motion of charged particles
35Q60 PDEs in connection with optics and electromagnetic theory
82C40 Kinetic theory of gases in time-dependent statistical mechanics
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