Asymptotic flocking dynamics for the kinetic Cucker-Smale model
Carrillo de la Plata, José Antonio (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Fornasier, Massimo (Johann Radon Institute for Computational and Applied Mathematics (Linz, Àustria))
Rosado Linares, Jesús (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Toscani, Giuseppe (University of Pavia. Department of Mathematics)
Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica

Imprint: Centre de Recerca Matemàtica 2009
Description: 22 p.
Abstract: 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.
Rights: 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 Creative Commons
Language: Anglès
Series: Centre de Recerca Matemàtica. Prepublicacions
Series: Prepublicacions del Centre de Recerca Matemàtica ; 886
Document: article ; submittedVersion
Subject: Equacions no lineals ; Anàlisi matemàtica ; Espais mètrics

Adreça alternativa:

22 p, 235.4 KB

The record appears in these collections:
Research literature > Preprints

 Record created 2010-04-14, last modified 2020-11-19

   Favorit i Compartir