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.
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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