- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:04
Interfaces and Free Boundaries
Interfaces Free Bound.
IFB
1463-9963
1463-9971
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
10.4171/IFB
http://www.ems-ph.org/doi/10.4171/IFB
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
14
2012
3
Existence and approximation of a nonlinear degenerate parabolic system modelling acid-mediated tumour invasion
John
Barrett
Imperial College London, LONDON, UNITED KINGDOM
Klaus
Deckelnick
Otto-von-Guericke-Universität Magdeburg, MAGDEBURG, GERMANY
Degenerate parabolic system, porous medium equation, existence, finite elements, tumour invasion
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.
Partial differential equations
Numerical analysis
General
343
363
10.4171/IFB/284
http://www.ems-ph.org/doi/10.4171/IFB/284