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|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|
|Electronic Publication Date:||3-Mar-2017|
|Citation:||Chazelle, B, Jiu, Q, Li, Q, Wang, C. (2017). Well-posedness of the limiting equation of a noisy consensus model in opinion dynamics. Journal of Differential Equations, 263 (365 - 397. doi:10.1016/j.jde.2017.02.036|
|Pages:||365 - 397|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||Journal of Differential Equations|
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