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On a coupled SDE-PDE system modeling acid-mediated tumor invasion

  • We propose and analyze a multiscale model for acid-mediated tumor invasion accounting for stochastic effects on the subcellular level. The setting involves a PDE of reaction-diffusion-taxis type describing the evolution of the tumor cell density, the movement being directed towards pH gradients in the local microenvironment, which is coupled to a PDE-SDE system characterizing the dynamics of extracellular and intracellular proton concentrations, respectively. The global well-posedness of the model is shown and numerical simulations are performed in order to illustrate the solution behavior.

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Verfasserangaben:Sandesh Athni Hiremath, Anna Zhigun, Stefanie Sonner, Christina Surulescu
URN (Permalink):urn:nbn:de:hbz:386-kluedo-44513
Sprache der Veröffentlichung:Englisch
Veröffentlichungsdatum (online):21.09.2016
Jahr der Veröffentlichung:2016
Veröffentlichende Institution:Technische Universität Kaiserslautern
Datum der Publikation (Server):22.09.2016
Fachbereiche / Organisatorische Einheiten:Fachbereich Mathematik
DDC-Sachgruppen:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Klassifikation (Mathematik):35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K59 Quasilinear parabolic equations
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Hxx Stochastic analysis [See also 58J65] / 60H10 Stochastic ordinary differential equations [See also 34F05]
92-XX BIOLOGY AND OTHER NATURAL SCIENCES / 92Cxx Physiological, cellular and medical topics / 92C17 Cell movement (chemotaxis, etc.)
Lizenz (Deutsch):Standard gemäß KLUEDO-Leitlinien vom 30.07.2015