We analyse the asymptotic behavior of solutions of the continuous kinetic version of flocking by Cucker and Smale, which describes the collective behavior of an ensemble of organisms, animals or devices. The kinetic version 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. It is proven that the solutions will concentrate exponentially fast their velocity to their mean while in space they will converge towards a translational flocking solution.
Asymptotic flocking dynamics for the kinetic Cucker-Smale model
TOSCANI, GIUSEPPE
2010-01-01
Abstract
We analyse the asymptotic behavior of solutions of the continuous kinetic version of flocking by Cucker and Smale, which describes the collective behavior of an ensemble of organisms, animals or devices. The kinetic version 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. It is proven that the solutions will concentrate exponentially fast their velocity to their mean while in space they will converge towards a translational flocking solution.File in questo prodotto:
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