Trend to equilibrium for a delay Vlasov-Fokker-Planck equation and explicit decay estimates

Axel Klar, Lisa Kreusser, Oliver Tse

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In this paper, a Vlasov-Fokker-Planck equation associated to a stochastic interacting particle system with distributed delay is analytically investigated. Under certain restrictions on the parameters, the well-posedness and equilibration of the Vlasov-Fokker-Planck equation are shown. Furthermore, an exponential rate of convergence toward an equilibrium measure is proven as long as the delay horizon is finite. For infinite delay horizon, i.e., when the entire history of the solution paths is taken into consideration, algebraic decay of the solution is shown.

Original languageEnglish
Pages (from-to)3277-3298
Number of pages22
JournalSiam Journal on Mathematical Analysis
Volume49
Issue number4
DOIs
Publication statusPublished - 29 Aug 2017

Keywords

  • Delay equations
  • Fibers
  • Interacting stochastic particles
  • Retarded mean-field equations
  • Trend to equilibrium
  • Vlasov-Fokker-Planck

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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