Zurück zu den Preprints des Jahres 2011


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

by Barrett, J.W.; Deckelnick, K..

Series: 2011-34, Preprints

35K55 Nonlinear parabolic equations
35K65 Degenerate parabolic equations
65M12 Stability and convergence of numerical methods
65M60 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods

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