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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