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Global existence for a degenerate haptotaxis model of cancer invasion

  • We propose and study a strongly coupled PDE-ODE system with tissue-dependent degenerate diffusion and haptotaxis that can serve as a model prototype for cancer cell invasion through the extracellular matrix. We prove the global existence of weak solutions and illustrate the model behaviour by numerical simulations for a two-dimensional setting.

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Verfasserangaben:Anna Zhigun, Christina Surulescu, Aydar Uatay
URN (Permalink):urn:nbn:de:hbz:386-kluedo-42324
Dokumentart:Preprint
Sprache der Veröffentlichung:Englisch
Veröffentlichungsdatum (online):27.11.2015
Jahr der Veröffentlichung:2015
Veröffentlichende Institution:Technische Universität Kaiserslautern
Datum der Publikation (Server):30.11.2015
Freies Schlagwort / Tag:cancer cell invasion; degenerate diffusion; global existence; haptotaxis; parabolic system; weak solution
Seitenzahl:25
Fachbereiche / Organisatorische Einheiten:Fachbereich Mathematik
DDC-Sachgruppen:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Klassifikation (Mathematik):35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B45 A priori estimates
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Dxx Generalized solutions / 35D30 Weak solutions
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K20 Initial-boundary value problems for second-order parabolic equations
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K51 Initial-boundary value problems for second-order parabolic systems
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K57 Reaction-diffusion equations
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K59 Quasilinear parabolic equations
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K65 Degenerate parabolic equations
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Qxx Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] / 35Q92 PDEs in connection with biology and other natural sciences
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