Stationary solutions of the Vlasov-Fokker-Planck equation: Existence, characterization and phase-transition

In this paper, we study the set of stationary solutions of the Vlasov-FokkerPlanck (VFP) equation. This equation describes the time evolution of the probability distribution of a particle moving under the influence of a doublewell 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.

• Type: Journal
• Year: 2016
• Where: APPML
• Authors: M. H. Duong, J. Tugaut
• Keywords: APPML 2016, Software Engineering