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IMA Journal of Applied Mathematics Advance Access originally published online on November 13, 2007
IMA Journal of Applied Mathematics 2008 73(1):69-106; doi:10.1093/imamat/hxm044
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© The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Population-scale modelling of cellular chemotaxis and aggregation

J. A. Fozard and J. R. King{dagger}

School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK

{dagger} Email: john.king{at}nottingham.ac.uk

Received on November 7, 2006; Accepted on May 4, 2007

Motivated by chemotaxis of, and especially aggregation within, populations of cells, we examine an extension of the Becker–Döring aggregation equations in which monomers undergo diffusion and advection in one spatial dimension, as well as attaching themselves to clusters of all sizes. We restrict our attention to irreversible aggregation, particularly for power-law rate coefficients. We examine the large-time behaviour of the initial-value problem on an infinite domain, both in the purely diffusive case and with advection. We also determine the large-time behaviour on a semi-infinite domain, with a non-zero Dirichlet condition imposed on the monomer concentration at the boundary. The asymptotic results are confirmed by numerical simulations.

Keywords: Becker–Döring equations; diffusion; convection; cellular aggregation; large-time asymptotics.


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