ASYMPTOTIC FLOCKING DYNAMICS FOR THE KINETIC CUCKER-SMALE MODEL

被引：403

作者：

Carrillo, J. A. ^{[1
]}

Fornasier, M. ^{[2
]}

Rosado, J. ^{[3
]}

Toscani, G. ^{[4
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, ICREA, Bellaterra 08193, Spain

[2] Johann Radon Inst Computat & Appl Math RICAM, A-4040 Linz, Austria

[3] Univ Autonoma Barcelona, Dept Matemat, Bellaterra 08193, Spain

[4] Univ Pavia, Dept Math, I-27100 Pavia, Italy

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2010年 / 42卷 / 01期

关键词：

flocking; nonlinear friction equations; mass transportation methods; CONTINUUM-LIMIT; BEHAVIOR; EQUATIONS; PARTICLE;

D O I：

10.1137/090757290

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we analyze the asymptotic behavior of solutions of the continuous kinetic version of flocking by Cucker and Smale [IEEE Trans. Automat. Control, 52 (2007), pp. 852-862], which describes the collective behavior of an ensemble of organisms, animals, or devices. This kinetic version introduced in [S.-Y. Ha and E. Tadmor, Kinet. Relat. Models, 1 (2008), pp. 415-435] 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 [ F. Cucker and S. Smale, IEEE Trans. Automat. Control, 52 (2007), pp. 852-862] is shown to hold for the solutions on the kinetic model. More precisely, the solutions will concentrate exponentially fast in velocity to the mean velocity of the initial condition, while in space they will converge towards a translational flocking solution.

引用

页码：218 / 236

页数：19

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