Coalescence of interacting cell populations

Abstract

We analyse the coalescence of invasive cell populations by studying both the temporal and steady behaviour of a system of coupled reaction-diffusion equations. This problem is relevant to recent experimental observations of the dynamics of opposingly directed invasion waves of cells. Two cell types, u and v, are considered with the cell motility governed by linear or nonlinear diffusion. The cells proliferate logistically so that the long-term total cell density, u + v approaches a carrying capacity. The steady-state solutions for u and v are denoted us and vs. The steady solutions are spatially invariant and satisfy us + vs = 1. However, this expression is underdetermined so the relative pr..