Global existence for chemotaxis with finite sampling radius

T. Hillen, K. Painter, C. Schmeiser

Research output: Contribution to journalArticlepeer-review

69 Citations (Scopus)


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 languageEnglish
Pages (from-to)125-144
Number of pages20
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number1
Publication statusPublished - Jan 2007


  • Chemotaxis
  • Finite sampling radius
  • Global existence
  • Non-local gradient


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