Nonlinearity Swarm dynamics and equilibria for a nonlocal aggregation model

@inproceedings{Fetecau2011NonlinearitySD,
  title={Nonlinearity Swarm dynamics and equilibria for a nonlocal aggregation model},
  author={Razvan C. Fetecau and Yanghong Huang and Theodore Kolokolnikov},
  year={2011}
}
We consider the aggregation equation ρt −∇ · (ρ∇K ∗ρ) = 0 in R, where the interaction potential K models short-range repulsion and long-range attraction. We study a family of interaction potentials for which the equilibria are of finite density and compact support. We show global well-posedness of solutions and investigate analytically and numerically the equilibria and their global stability. In particular, we consider a potential for which the corresponding equilibrium solutions are of… CONTINUE READING
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