Liapunov functionals and large-time-asymptotics of mean-field nonlinear Fokker-Planck equations

Anton Arnold*, Luis L. Bonilla, Peter Markowich

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

Large-time asymptotics of the solutions of time-dependent mean-field nonlinear Fokker-Planck systems are analyzed by exploiting the properties of Liapunov functionals (relative entropies). We first discuss the scalar Desai-Zwanzig model and then generalize the techniques to a general class of mean-field oscillator equations. Systems of this type are relevant in the modeling of synchronization of a large population of coupled nonlinear oscillators in the presence of external or thermal white noise.

Original languageEnglish (US)
Pages (from-to)733-751
Number of pages19
JournalTransport Theory and Statistical Physics
Volume25
Issue number7
DOIs
StatePublished - Jan 1 1996

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Transportation
  • Physics and Astronomy(all)
  • Applied Mathematics

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