Global solvability and explicit bounds for non-local adhesion models

Thomas Hillen, Kevin J. Painter, M. Winkler

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)
46 Downloads (Pure)


Adhesion between cells and other cells (cell-cell adhesion) or other tissue components (cell-matrix adhesion) is an intrinsically non-local phenomenon. Consequently, a number of recently developed mathematical models for cell adhesion have taken the form of non-local partial differential equations, where the non-local term arises inside a spatial derivative. The mathematical properties of such a non-local gradient term are not yet well understood. Here we use sophisticated estimation techniques to show local and global existence of classical solutions for such examples of adhesion-type models, and we provide a uniform upper bound for the solutions. Further, we discuss the significance of these results to applications in cell sorting and in cancer invasion and support the theoretical results through numerical simulations.

Original languageEnglish
Pages (from-to)645-684
Number of pages40
JournalEuropean Journal of Applied Mathematics
Issue number4
Early online date23 Nov 2017
Publication statusPublished - Aug 2018


  • adhesion
  • cancer invasion
  • existence and uniqueness
  • non-local PDE
  • uniform bounds

ASJC Scopus subject areas

  • Applied Mathematics


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