Abstract
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 language | English (US) |
|---|---|
| Pages (from-to) | 365-397 |
| Number of pages | 33 |
| Journal | Journal of Differential Equations |
| Volume | 263 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jul 5 2017 |
| Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics
Keywords
- Global stability
- Hegselmann–Krause model
- Nonlinear Fokker–Planck equation
- Well-posedness
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