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MiS Preprint
5/2007

An Integro-Differential Equation Model for Alignment and Orientational Aggregation

Kyungkeun Kang, Benoit Perthame, Angela Stevens and Juan J.L. Velazquez

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 [J. Math. Biol. 46 (2003), no. 6, 537--563].

Here we analyze the time dependent problem and prove that the type of alignment (one or multidirectional) 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.

Received:
Jan 18, 2007
Published:
Jan 18, 2007
Keywords:
kinetic equations, asymptotic behavior, alignment of cells and filaments

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2009 Repository Open Access
Kyungkeun Kang, Benoît Perthame, Angela Stevens and Juan J. L. Velázquez

An integro-differential equation model for alignment and orientational aggregation

In: Journal of differential equations, 246 (2009) 4, pp. 1387-1421