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Periodic solutions of the Vlasov-Poisson system with boundary conditions. (Solutions périodiques du système de Vlasov-Poisson avec conditions aux limites.) (French) Zbl 0895.35079
Summary: We study here the 1D Vlasov-Poisson system with time periodic boundary conditions. We prove the existence of time periodic solutions. The crucial assumption is that the particles are injected with velocity large enough with respect to the electric field, so that every particle crosses the domain in a finite time.

MSC:
35Q35 PDEs in connection with fluid mechanics
35B10 Periodic solutions to PDEs
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
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