Global existence for chemotaxis with finite sampling radius

Abstract

Migrating cells measure the external environment through receptor-binding of specific chemicals at their outer cell membrane. In this paper this non-local sampling is incorporated into a chemotactic model. The existence of global bounded solutions of the non-local model is proven for bounded and unbounded domains in any space dimension. According to a recent classification of spikes and plateaus, it is shown that steady state solutions cannot be of spike-type. Finally, numerical simulations support the theoretical results, illustrating the ability of the model to give rise to pattern formation. Some biologically relevant extensions of the model are also considered.