Mesenchymal motion models in one dimension

Zhian Wang, Thomas Hillen, Michael Li

Research output: Journal article publicationJournal articleAcademic researchpeer-review

6 Citations (Scopus)

Abstract

Mesenchymal motion denotes a form of cell movement through tissue which can be observed for certain cancer metastases. In [T. Hillen, J. Math. Biol., 53 (2006), pp. 585-616], a mathematical model for this form of movement was introduced. In the current paper we present a comprehensive analysis of the one-dimensional mesenchymal motion model. We establish the global existence of classical solutions and rigorously carry out the parabolic limit of the model. We discuss the stationary solutions, prove the existence of traveling wave solutions, and use numerical simulations to illustrate the results. Finally, we discuss the biological implications of the results.
Original languageEnglish
Pages (from-to)375-397
Number of pages23
JournalSIAM Journal on Applied Mathematics
Volume69
Issue number2
DOIs
Publication statusPublished - 13 Nov 2008
Externally publishedYes

Keywords

  • Global existence
  • Hyperbolic systems
  • Macroscopic limits
  • Mesenchymal motion
  • Stationary solutions
  • Traveling waves

ASJC Scopus subject areas

  • Applied Mathematics

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