Explicit equilibrium solutions for the aggregation equation with power-law potentials

Research output: Contribution to journalArticle

Abstract

Despite their wide presence in various models in the study of collective
behaviors, explicit swarming patterns are difficult to obtain. In this
paper, special stationary solutions of the aggregation equation with power-law
kernels are constructed by inverting Fredholm integral operators or by employing
certain integral identities. These solutions are expected to be the global
energy stable equilibria and to characterize the generic behaviors of stationary
solutions for more general interactions.

Bibliographical metadata

Original languageEnglish
Pages (from-to)171 - 192
Number of pages22
JournalKinetic and Related Models
Volume10
Issue number1
Early online date30 Nov 2016
DOIs
StatePublished - 1 Mar 2017