# American Institute of Mathematical Sciences

January  2007, 7(1): 125-144. doi: 10.3934/dcdsb.2007.7.125

## Global existence for chemotaxis with finite sampling radius

 1 University of Alberta, Edmonton, Alberta, Canada T6G 2G1, Canada 2 Heriot-Watt University, Edinburgh, EH11 1UF, United Kingdom 3 University of Vienna, Faculty for Mathematics, Nordbergstraße 15, 1090 Wien, Austria

Received  January 2006 Revised  September 2006 Published  October 2006

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.
Citation: T. Hillen, K. Painter, Christian Schmeiser. Global existence for chemotaxis with finite sampling radius. Discrete & Continuous Dynamical Systems - B, 2007, 7 (1) : 125-144. doi: 10.3934/dcdsb.2007.7.125
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