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

Handle URI:
http://hdl.handle.net/10754/597626
Title:
Asymptotic stability of constant steady states for a 2×2 reaction–diffusion system arising in cancer modelling
Authors:
Di Francesco, Marco; Twarogowska, Monika
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.
Citation:
Di Francesco M, 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: 1457–1468. Available: http://dx.doi.org/10.1016/j.mcm.2010.03.034.
Publisher:
Elsevier BV
Journal:
Mathematical and Computer Modelling
Issue Date:
Apr-2011
DOI:
10.1016/j.mcm.2010.03.034
Type:
Article
ISSN:
0895-7177
Sponsors:
MDF acknowledges support from the KAUST award of Prof. Peter A. Markowich (University of Cambridge). The authors are grateful to Prof. Luigi Preziosi for helpful suggestions and comments. Part of this work was performed when the authors were attending an advanced course in Biomathematics at CRM (Autonomous University of Barcelona): they are grateful to the organizers for their support. Finally, the authors would like to thank the two referees for their useful suggestions on the improvement of the paper.
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Full metadata record

DC FieldValue Language
dc.contributor.authorDi Francesco, Marcoen
dc.contributor.authorTwarogowska, Monikaen
dc.date.accessioned2016-02-25T12:43:17Zen
dc.date.available2016-02-25T12:43:17Zen
dc.date.issued2011-04en
dc.identifier.citationDi Francesco M, 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: 1457–1468. Available: http://dx.doi.org/10.1016/j.mcm.2010.03.034.en
dc.identifier.issn0895-7177en
dc.identifier.doi10.1016/j.mcm.2010.03.034en
dc.identifier.urihttp://hdl.handle.net/10754/597626en
dc.description.abstractThe 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.en
dc.description.sponsorshipMDF acknowledges support from the KAUST award of Prof. Peter A. Markowich (University of Cambridge). The authors are grateful to Prof. Luigi Preziosi for helpful suggestions and comments. Part of this work was performed when the authors were attending an advanced course in Biomathematics at CRM (Autonomous University of Barcelona): they are grateful to the organizers for their support. Finally, the authors would like to thank the two referees for their useful suggestions on the improvement of the paper.en
dc.publisherElsevier BVen
dc.subjectAsymptotic stabilityen
dc.subjectCancer modelingen
dc.subjectChemotaxisen
dc.subjectCross diffusionen
dc.subjectReaction-diffusion systemsen
dc.titleAsymptotic stability of constant steady states for a 2×2 reaction–diffusion system arising in cancer modellingen
dc.typeArticleen
dc.identifier.journalMathematical and Computer Modellingen
dc.contributor.institutionUniversita degli Studi dell'Aquila, L'Aquila, Italyen
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