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Global Well-posedness of the Spatially Homogeneous Kolmogorov-Vicsek Model as a Gradient Flow

Authors
Figalli, AlessioKang, Moon-JinMorales, Javier
Issue Date
Mar-2018
Publisher
SPRINGER
Citation
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, v.227, no.3, pp 869 - 896
Pages
28
Journal Title
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
Volume
227
Number
3
Start Page
869
End Page
896
URI
https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/4622
DOI
10.1007/s00205-017-1176-2
ISSN
0003-9527
1432-0673
Abstract
We consider the so-called spatially homogenous Kolmogorov-Vicsek model, a non-linear Fokker-Planck equation of self-driven stochastic particles with orientation interaction under the space-homogeneity. We prove the global existence and uniqueness of weak solutions to the equation. We also show that weak solutions exponentially converge to a steady state, which has the form of the Fisher-von Mises distribution.
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