Population-scale modelling of cellular chemotaxis and aggregation

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