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

M. Di Francesco; M. Twarogowska

doi:10.1016/j.mcm.2010.03.034

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

M. Di Francesco
, M. Twarogowska

Department of Mathematical Sciences

Università degli Studi dell'Aquila

Research output: Contribution to journal › Article › peer-review

2 Citations (SciVal)

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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.

Original language	English
Pages (from-to)	1457-1468
Number of pages	12
Journal	Mathematical and Computer Modelling
Volume	53
Issue number	7-8
DOIs	https://doi.org/10.1016/j.mcm.2010.03.034
Publication status	Published - 1 Apr 2011

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10.1016/j.mcm.2010.03.034

Author's accepted version
NOTICE: this is the author’s version of a work that was accepted for publication in Mathematical and Computer Modelling. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Mathematical and Computer Modelling, vol 53, issue 7-8. 2011, DOI 10.1016/j.mcm.2010.03.034
Accepted author manuscript, 210 KB

Cite this

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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.",

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AB - 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.

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

Abstract

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