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

Global existence for chemotaxis with finite sampling radius

T. Hillen 1, , K. Painter 2, and  Christian Schmeiser 3,

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.
Keywords: Finite Sampling Radius, Non-local Gradient., Chemotaxis, Global Existence.
Mathematics Subject Classification: Primary: 92C17 Secondary: 35K1.
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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