Analysis of propagating pattern in a chemotaxis system.

We consider a cell-chemotaxis model which can generate spatially heterogeneous patterns in cell density and chemoattractant. A local perturbation about the uniform steady state propagates across the domain leaving behind a steady state pattern of standing peaks and troughs. We investigate this patterning process analytically and obtain estimates for the pattern wavelength and speed of spread. We compare the analytical results with numerical simulation of the full model systems.