Existence and uniqueness of global classical solutions to a two dimensional two species cancer invasion haptotaxis model

Jan Giesselmann, Niklas Kolbe, Mária Lukáčová-Medvidová, Nikolaos Sfakianakis

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

We consider a haptotaxis cancer invasion model that includes two families of cancer cells. Both families migrate on the extracellular matrix and proliferate. Moreover the model describes an epithelial-to-mesenchymal-like transition between the two families, as well as a degradation and a self-reconstruction process of the extracellular matrix. We prove in two dimensional space positivity and conditional global existence and uniqueness of the classical solutions of the problem for large initial data.

Original languageEnglish
Pages (from-to)4397-4431
Number of pages35
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume23
Issue number10
Early online date30 Jun 2018
DOIs
Publication statusPublished - Dec 2018

Keywords

  • Advection-reaction-diffusion
  • Cancer stem cells
  • Classical solutions
  • Haptotaxis model
  • Invasion of the extracellular matrix

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