Existence and approximation of a nonlinear degenerate parabolic system modelling acid-mediated tumour invasion
Preprint series: 11-34, Preprints
- 35K55 Nonlinear PDE of parabolic type
- 35K65 Parabolic partial differential equations of degenerate type
- 65M12 Stability and convergence of numerical methods
- 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
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 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.
Keywords: Degenerate parabolic system, porous medium equation, existence, finite elements, tumour invasion
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