Poupaud, Frédéric Boundary value problems for the stationary Vlasov-Maxwell system. (English) Zbl 0785.35020 Forum Math. 4, No. 5, 499-527 (1992). 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. Cited in 28 Documents 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 Keywords:Vlasov-Maxwell equations; self-consistent electromagnetic field; existence of stationary solutions; upper solutions PDFBibTeX XMLCite \textit{F. Poupaud}, Forum Math. 4, No. 5, 499--527 (1992; Zbl 0785.35020) Full Text: DOI EuDML