Asymptotic stability of constant steady states for a 2×2 reaction–diffusion system arising in cancer modelling

Marco Di Francesco, Monika Twarogowska

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

The dependence of tumor on essential nutrients is known to be crucial for its evolution and has become one of the targets for medical therapies. Based on this fact a reaction-diffusion system with chemotaxis term and nutrient-based growth of tumors is presented. The formulation of the model considers also an influence of tumor and pharmacological factors on nutrient concentration. In the paper, convergence of solutions to constant, stationary states in the one-dimensional case for small perturbation of the equilibria is investigated. The nonlinear stability results are obtained by means of the classical symmetrization method and energy Sobolev estimates. © 2010 Elsevier Ltd.
Original languageEnglish (US)
Pages (from-to)1457-1468
Number of pages12
JournalMathematical and Computer Modelling
Volume53
Issue number7-8
DOIs
StatePublished - Apr 2011
Externally publishedYes

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