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- W4299443637 abstract "In this paper, we study the set of stationary solutions of the Vlasov-Fokker-Planck (VFP) equation. This equation describes the time evolution of the probability distribution of a particle moving under the influence of a double-well potential, an interaction potential, a friction force and a stochastic force. We prove, under suitable assumptions, that the VFP equation does not have a unique stationary solution and that there exists a phase transition. Our study relies on the recent results by Tugaut and coauthors regarding the McKean-Vlasov equation." @default.
- W4299443637 created "2022-10-02" @default.
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- W4299443637 date "2015-05-05" @default.
- W4299443637 modified "2023-09-23" @default.
- W4299443637 title "Stationary solutions of the Vlasov-Fokker-Planck equation: existence, characterization and phase-transition" @default.
- W4299443637 doi "https://doi.org/10.48550/arxiv.1505.01212" @default.
- W4299443637 hasPublicationYear "2015" @default.
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