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Global existence for a degenerate haptotaxis model of tumor invasion under the go-or-grow dichotomy hypothesis

  • We propose and study a strongly coupled PDE-ODE-ODE system modeling cancer cell invasion through a tissue network under the go-or-grow hypothesis asserting that cancer cells can either move or proliferate. Hence our setting features two interacting cell populations with their mutual transitions and involves tissue-dependent degenerate diffusion and haptotaxis for the moving subpopulation. The proliferating cells and the tissue evolution are characterized by way of ODEs for the respective densities. We prove the global existence of weak solutions and illustrate the model behaviour by numerical simulations in a two-dimensional setting.

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Author:Anna Zhigun, Christina Surulescu, Alexander Hunt
URN (permanent link):urn:nbn:de:hbz:386-kluedo-43844
Document Type:Preprint
Language of publication:English
Publication Date:2016/05/30
Year of Publication:2016
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2016/05/31
Tag:cancer cell invasion; degenerate diffusion; global existence; go-or-grow dichotomy; haptotaxis; parabolic system; weak solution
Number of page:23
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):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.)
Licence (German):Standard gemäß KLUEDO-Leitlinien vom 30.07.2015