BOUNDARY-VALUE-PROBLEMS FOR THE STATIONARY VLASOV-MAXWELL SYSTEM

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 classic mechanics, systems with several species of particles and Boltzmann-Vlasov-Poisson problems.