Heriot-Watt Mathematics Report Series
HWM06-24, 5 May 2006

Global Existence for Chemotaxis with Finite Sampling Radius

T Hillen, K Painter and C Schmeiser


Abstract

Migrating cells measure the external environment through receptor-binding of specific chemicals at their outer cell membrane. In this paper we incorporate this non-local sampling into a chemotactic model. We prove that, in contrast to the classical chemotaxis model, the non-local model has globally existing solutions for any space dimension. We use a classification of spikes and plateaus and show that steady state solutions cannot be of spike-type. Finally, we use numerical simulations to support the theoretical results, illustrate the ability of the model to give rise to pattern formation and consider some biologically relevent extensions of the model.

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