Long-Time Dynamics for a Simple Aggregation Equation on the Sphere


Conference Paper

© Springer Nature Switzerland AG 2019. We give a complete study of the asymptotic behavior of a simple model of alignment of unit vectors, both at the level of particles, which corresponds to a system of coupled differential equations, and at the continuum level, under the form of an aggregation equation on the sphere. We prove unconditional convergence towards an aligned asymptotic state. In the cases of the differential system and of symmetric initial data for the partial differential equation, we provide precise rates of convergence.

Full Text

Duke Authors

Cited Authors

  • Frouvelle, A; Liu, JG

Published Date

  • January 1, 2019

Published In

Volume / Issue

  • 282 /

Start / End Page

  • 457 - 479

Electronic International Standard Serial Number (EISSN)

  • 2194-1017

International Standard Serial Number (ISSN)

  • 2194-1009

International Standard Book Number 13 (ISBN-13)

  • 9783030150952

Digital Object Identifier (DOI)

  • 10.1007/978-3-030-15096-9_16

Citation Source

  • Scopus