Duong, Manh HongManh HongDuongTugaut, JulianJulianTugaut2018-05-172018-03-152018-05-172018-03-15Electronic Communications in Probability, 2018, 231083-589Xhttp://hdl.handle.net/10044/1/59200In this paper, we study the long-time behaviour of solutions to the Vlasov-Fokker-Planck equation where the confining potential is non-convex. This is a nonlocal nonlinear partial differential equation describing the time evolution of the probability distribution of a particle moving under the influence of a non-convex potential, an interaction potential, a friction force and a stochastic force. Using the free-energy approach, we show that under suitable assumptions solutions of the Vlasov-Fokker-Planck equation converge to an invariant probability.© 2018 The Authors. Available under a Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/).Science & TechnologyPhysical SciencesStatistics & ProbabilityMathematicskinetic equationVlasov-Fokker-Planck equationfree-energyasymptotic behaviourgranular media equationstochastic processesSELF-STABILIZING PROCESSESMULTI-WELLS LANDSCAPEGRANULAR MEDIABEHAVIORFIELDMODEL0104 StatisticsJournal Articlehttps://www.dx.doi.org/10.1214/18-ECP116https://doi.org/10.1214/18-ECP116