Well-posedness of the limiting equation of a noisy consensus model in opinion dynamics

Bernard Chazelle, Quansen Jiu, Qianxiao Li, Chu Wang

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


This paper establishes the global well-posedness of the nonlinear Fokker–Planck equation for a noisy version of the Hegselmann–Krause model. The equation captures the mean-field behavior of a classic multiagent system for opinion dynamics. We prove the global existence, uniqueness, nonnegativity and regularity of the weak solution. We also exhibit a global stability condition, which delineates a forbidden region for consensus formation. This is the first nonlinear stability result derived for the Hegselmann–Krause model.

Original languageEnglish (US)
Pages (from-to)365-397
Number of pages33
JournalJournal of Differential Equations
Issue number1
StatePublished - Jul 5 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics


  • Global stability
  • Hegselmann–Krause model
  • Nonlinear Fokker–Planck equation
  • Well-posedness


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