The Vlasov-Fokker-Planck equation in non-convex landscapes: Convergence to equilibrium

M.H. Duong, J. Tugaut

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
111 Downloads (Pure)

Abstract

In 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.
Original languageEnglish
Article number19
Number of pages10
JournalElectronic Communications in Probability
Volume23
DOIs
Publication statusPublished - 15 Mar 2018

Keywords

  • Kinetic equation
  • Vlasov-Fokker-Planck equation
  • Free-energy
  • Asymptotic behaviour
  • Granular media equation
  • Stochastic processes

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