Nonlocal and local models for taxis in cell migration: a rigorous limit procedure

Maria Eckardt, Kevin J. Painter, Christina Surulescu, Anna Zhigun

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
2 Downloads (Pure)

Abstract

A rigorous limit procedure is presented which links nonlocal models involving adhesion or nonlocal chemotaxis to their local counterparts featuring haptotaxis and classical chemotaxis, respectively. It relies on a novel reformulation of the involved nonlocalities in terms of integral operators applied directly to the gradients of signal-dependent quantities. The proposed approach handles both model types in a unified way and extends the previous mathematical framework to settings that allow for general solution-dependent coefficient functions. The previous forms of nonlocal operators are compared with the new ones introduced in this paper and the advantages of the latter are highlighted by concrete examples. Numerical simulations in 1D provide an illustration of some of the theoretical findings.

Original languageEnglish
Pages (from-to)1251-1298
Number of pages48
JournalJournal of Mathematical Biology
Volume81
Issue number6-7
Early online date17 Oct 2020
DOIs
Publication statusPublished - Dec 2020

Keywords

  • Cell–cell and cell–tissue adhesion
  • Global existence
  • Haptotaxis
  • Integro-differential equations
  • Nonlocal and local chemotaxis
  • Rigorous limit behaviour
  • Unified approach
  • Weak solutions

ASJC Scopus subject areas

  • Modelling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics

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