by Barrett, J.W.; Deckelnick, K..
Series: 2011-34, Preprints
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 H+ ions. We obtain an existence result for the system by constructing a suitable finite element approximation and analysing its convergence. Finally, we report on corresponding numerical experiments.
Degenerate parabolic system, porous medium equation, existence, finite elements, tumour invasion