Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 263, Issue 1, Pages 365-397Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2017.02.036
Keywords
Hegselmann-Krause model; Nonlinear Fokker-Planck equation; Well-posedness; Global stability
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Funding
- NSF [CCF-0963825, CCF-1016250, CCF-1420112]
- National Natural Sciences Foundation of China [11171229, 11231006]
- Project of Beijing Chang Cheng Xue Zhe
- Agency for Science, Technology and Research, Singapore
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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 multi agent system for opinion dyrignics. 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. (C) 2017 Elsevier Inc. All rights reserved.
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