ASYMPTOTIC FLOCKING DYNAMICS FOR THE KINETIC CUCKER-SMALE MODEL
ASYMPTOTIC FLOCKING DYNAMICS FOR THE KINETIC CUCKER-SMALE MODEL
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DOI：
10.1137/090757290
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发表时间：
2010-01-01
影响因子：
2
通讯作者：
Toscani, G.
中科院分区：
文献类型：
--
作者：
Carrillo, J. A.;Fornasier, M.;Toscani, G.
在这篇文章中，我们分析了Cucker和Smear[IEEE Transans]提出的连续动力学形式的群集问题解的渐近行为。自动的。控制，52(2007)，第852-862页]，描述了一组生物、动物或装置的集体行为。这一动力学版本在[S.Y.Ha和E.Tadamor，Kine.]中介绍。雷拉特。Models，1(2008)，pp.415-435]是从Boltzmann型方程出发得到的。然后利用粒子近似和度量距离的稳定性研究了相空间分布的大时间行为。对[F·Cucker和S·Smer，IEEE译文]的定理进行了连续类比。自动的。Control，52(2007)，pp.852-862]被证明对动力学模型上的解成立。更准确地说，解将以指数级的速度集中到初始条件的平均速度，而在空间中，它们将收敛到平移群集解。
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.