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.
Original language | English |
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Pages (from-to) | 125-144 |
Number of pages | 20 |
Journal | Discrete and Continuous Dynamical Systems - Series B |
Volume | 7 |
Issue number | 1 |
DOIs | |
Publication status | Published - Jan 2007 |
Keywords
- Chemotaxis
- Finite sampling radius
- Global existence
- Non-local gradient