Mathematical analysis of a kinetic model for cell movement in network tissues

Thomas Hillen, Peter Hinow, Zhian Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

14 Citations (Scopus)

Abstract

Mesenchymal motion describes the movement of cells in biological tissues formed by fibre networks. An important example is the migration of tumour cells through collagen networks during the process of metastasis formation. We investigate the mesenchymal motion model proposed by T. Hillen in [14] in higher dimensions. We formulate the problem as an evolution equation in a Banach space of measure-valued functions and use methods from semigroup theory to show the global existence of mild and classical solutions. We investigate steady states of the model and show that patterns of network type exist as steady states. For the case of constant fibre distribution, we find an explicit solution and we prove the convergence to the parabolic limit.
Original languageEnglish
Pages (from-to)1055-1080
Number of pages26
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume14
Issue number3
DOIs
Publication statusPublished - 1 Oct 2010
Externally publishedYes

Keywords

  • Kinetic theory
  • Mesenchymal motion
  • Parabolic limits
  • Pointwise steady states

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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