Global Weak Solutions for Kolmogorov-Vicsek Type Equations with Orientational Interactions

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We study the global existence and uniqueness of weak solutions to kinetic Kolmogorov-Vicsek models that can be considered as non-local, non-linear, Fokker-Planck type equations describing the dynamics of individuals with orientational interactions. This model is derived from the discrete Couzin-Vicsek algorithm as mean-field limit (Bolley et al., Appl Math Lett, 25:339-343, 2012; Degond et al., Math Models Methods Appl Sci 18:1193-1215, 2008), which governs the interactions of stochastic agents moving with a velocity of constant magnitude, that is, the corresponding velocity space for these types of Kolmogorov-Vicsek models is the unit sphere. Our analysis for L (p) estimates and compactness properties take advantage of the orientational interaction property, meaning that the velocity space is a compact manifold.
Publisher
SPRINGER
Issue Date
2016-10
Language
English
Article Type
Article
Citation

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, v.222, no.1, pp.317 - 342

ISSN
0003-9527
DOI
10.1007/s00205-016-1002-2
URI
http://hdl.handle.net/10203/278728
Appears in Collection
MA-Journal Papers(저널논문)
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