Existence of piecewise weak solutions of a discrete Cucker-Smale's flocking model with a singular communication weight

Jan Peszek

Existence of piecewise weak solutions of a discrete Cucker-Smale's flocking model with a singular communication weight

Analysis of PDEs 2013-02-19 v1

Authors: Jan Peszek

Abstract

We prove existence of global $C^1$ piecewise weak solutions for the discrete Cucker-Smale's flocking model with the communication weight $\psi(s)=s^{-\alpha}, 0<\alpha<1.$ We also discuss the possibility of finite in time alignment of the velocities of the particles.

Keywords

Cucker-Smale model flocking model piecewise weak solutions singular communication weight velocity alignment discrete system

Cite

@article{arxiv.1302.4224,
  title  = {Existence of piecewise weak solutions of a discrete Cucker-Smale's flocking model with a singular communication weight},
  author = {Jan Peszek},
  journal= {arXiv preprint arXiv:1302.4224},
  year   = {2013}
}

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