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

John W. Barrett | Zendy; Klaus Deckelnick | Zendy

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

Author(s) -

John W. Barrett,

Klaus Deckelnick

Publication year - 2012

Publication title -

interfaces and free boundaries mathematical analysis computation and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.964

H-Index - 39

eISSN - 1463-9971

pISSN - 1463-9963

DOI - 10.4171/ifb/284

Subject(s) - degenerate energy levels , parabolic partial differential equation , nonlinear system , convergence (economics) , reaction–diffusion system , mathematics , mathematical analysis , finite element method , diffusion , physics , partial differential equation , thermodynamics , quantum mechanics , economics , economic growth

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.

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