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

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


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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Letzte Änderung: 01.03.2018 - Ansprechpartner:

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