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Long-time dynamics for a simple aggregation equation on the sphere

Frouvelle, Amic; Liu, Jian-Guo (2018), Long-time dynamics for a simple aggregation equation on the sphere. https://basepub.dauphine.fr/handle/123456789/18455

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-01894368
Date
2018
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Pages
22
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Author(s)
Frouvelle, Amic cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Liu, Jian-Guo
Duke Physics
Abstract (EN)
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.
Subjects / Keywords
alignment; unit vectors; aggregation equation