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

M.H. Duong, J. Tugaut

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)38-45
Number of pages8
JournalApplied Mathematics Letters
Volume52
Early online date15 Aug 2015
DOIs
Publication statusPublished - Feb 2016

Keywords

  • Invariant measure
  • Vlasov–Fokker–Planck equation
  • McKean–Vlasov equation
  • Stochastic processes

Fingerprint

Dive into the research topics of 'Stationary solutions of the Vlasov-Fokker-Planck equation: Existence, characterization and phase-transition'. Together they form a unique fingerprint.

Cite this