An integro-differential equation model for alignment and orientational aggregation

Kyungkeun Kang, Benoit Perthame, Angela Stevens, J. J.L. Velázquez

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

We study an integro-differential equation modeling angular alignment of interacting bundles of cells or filaments. A bifurcation analysis of the related stationary problem was done by Geigant and Stoll in [E. Geigant, M. Stoll, Bifurcation analysis of an orientational aggregation model, J. Math. Biol. 46 (6) (2003) 537-563]. Here we analyze the time-dependent problem and prove that the type of alignment (one- or multi-directional) depends on the initial distribution, the interaction potential, and the preferred optimal orientation of the bundles of cells or filaments. Our main technical tool is the analysis of the evolution of suitable functionals for the cell density, which allows to also specify the direction(s) where the final alignment takes place.

Original languageEnglish
Pages (from-to)1387-1421
Number of pages35
JournalJournal of Differential Equations
Volume246
Issue number4
DOIs
Publication statusPublished - 2009 Feb 15

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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