JournalsifbVol. 14, No. 3pp. 343–363

Existence and approximation of a nonlinear degenerate parabolic system modelling acid-mediated tumour invasion

  • John W. Barrett

    Imperial College London, United Kingdom
  • Klaus Deckelnick

    Otto-von-Guericke-Universität Magdeburg, Germany
Existence and approximation of a nonlinear degenerate parabolic system modelling acid-mediated tumour invasion cover
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Abstract

We consider a nonlinear parabolic system of reaction–diffusion equations modelling acid-mediated tumour invasion. The system couples potentially degenerate equations for the cell densities of the normal and tumour populations to a parabolic equation for the concentration of HC ions. We obtain an existence result for the system by constructing a suitable finite element approximation and analyzing its convergence. Finally, we report on corresponding numerical experiments.

Cite this article

John W. Barrett, Klaus Deckelnick, Existence and approximation of a nonlinear degenerate parabolic system modelling acid-mediated tumour invasion. Interfaces Free Bound. 14 (2012), no. 3, pp. 343–363

DOI 10.4171/IFB/284