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


Reference:

Di Francesco, M. and Twarogowska, M., 2011. Asymptotic stability of constant steady states for a 2 2 reaction-diffusion system arising in cancer modelling. Mathematical and Computer Modelling, 53 (7-8), pp. 1457-1468.

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    Official URL:

    http://dx.doi.org/10.1016/j.mcm.2010.03.034

    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.

    Details

    Item Type Articles
    CreatorsDi Francesco, M.and Twarogowska, M.
    DOI10.1016/j.mcm.2010.03.034
    DepartmentsFaculty of Science > Mathematical Sciences
    Publisher StatementDiFrancesco_Twarogowska.pdf: 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
    RefereedYes
    StatusPublished
    ID Code32320

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