Duan, Renjun; Liu, Shuangqian Time-periodic solutions of the Vlasov-Poisson-Fokker-Planck system. (English) Zbl 1340.35348 Acta Math. Sci., Ser. B, Engl. Ed. 35, No. 4, 876-886 (2015). Summary: In this note it is shown that the Vlasov-Poisson-Fokker-Planck system in the three-dimensional whole space driven by a time-periodic background profile near a positive constant state admits a time-periodic small-amplitude solution with the same period. The proof follows by the Serrin’s method on the basis of the exponential time-decay property of the linearized system in the case of the constant background profile. Cited in 7 Documents MSC: 35Q84 Fokker-Planck equations 82D10 Statistical mechanics of plasmas Keywords:Vlasov-Poisson-Fokker-Planck system; time-periodic solution; energy method; exponential time-decay PDFBibTeX XMLCite \textit{R. Duan} and \textit{S. Liu}, Acta Math. Sci., Ser. B, Engl. Ed. 35, No. 4, 876--886 (2015; Zbl 1340.35348) Full Text: DOI