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Periodic solutions of the 1D Vlasov-Maxwell system with boundary conditions. (English) Zbl 0965.35010
The authors study the 1D Vlasov-Maxwell system with time-periodic boundary conditions in its classical and relativistic form. The main goal of the paper is to prove existence result for the weak periodic solution. The main mathematical difficulty consists of establishing $$L^\infty$$-estimates for the charge and current densities. Then the authors construct the regularized system, which leads to a sequence of approximate solutions. The existence proof uses the Schauder fixed point theorem for the modified problem. Then the passage to the limit in the regularization parameter leads to the main result. The last section treats the relativistic case.

##### MSC:
 35B10 Periodic solutions to PDEs 82D10 Statistical mechanical studies of plasmas
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