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Title:
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Asymptotic flocking dynamics for the kinetic Cucker-Smale model
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Author:
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Carrillo, José A.; Fornasier, Massimo; Rosado, Jesús; Toscani, Giuseppe
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Other authors:
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Centre de Recerca Matemàtica |
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Resum:
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In this paper, we analyse the asymptotic behavior of solutions of the continuous kinetic version of flocking by Cucker and Smale [16], which describes the collective behavior of an ensemble of organisms, animals or devices. This kinetic version introduced in [24] is here obtained starting from a Boltzmann-type equation. The large-time behavior of the distribution in
phase space is subsequently studied by means of particle approximations and a stability property in distances between measures. A continuous analogue of the theorems of [16] is shown to hold for the solutions on the kinetic model.
More precisely, the solutions will concentrate exponentially fast their velocity
to their mean while in space they will converge towards a translational flocking
solution. |
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Publication date:
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2009-10 |
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Subject (UDC):
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517 - Anàlisi |
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Subject(s):
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Equacions no lineals
Anàlisi matemàtica
Espais mètrics |
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Rights:
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Aquest document està subjecte a una llicència d'ús de Creative Commons, amb la qual es permet copiar, distribuir i comunicar públicament l'obra sempre que se'n citin l'autor original, la universitat i el centre i no se'n faci cap ús comercial ni obra derivada, tal com queda estipulat en la llicència d'ús (http://creativecommons.org/licenses/by-nc-nd/2.5/es/) |
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Document type:
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Preprint |
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