Asymptotic flocking dynamics for the kinetic Cucker-Smale model


Autoria(s): Carrillo, José A.; Fornasier, Massimo; Rosado, Jesús; Toscani, Giuseppe
Contribuinte(s)

Centre de Recerca Matemàtica

Data(s)

01/10/2009

Resumo

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.

Formato

22

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Identificador

http://hdl.handle.net/2072/46770

Idioma(s)

eng

Publicador

Centre de Recerca Matemàtica

Relação

Prepublicacions del Centre de Recerca Matemàtica;886

Direitos

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Palavras-Chave #Equacions no lineals #Anàlisi matemàtica #Espais mètrics #517 - Anàlisi
Tipo

info:eu-repo/semantics/preprint