Global existence for a go-or-grow multiscale model for tumor invasion with therapy

  • We investigate a PDE-ODE system describing cancer cell invasion in a tissue network. The model is an extension of the multiscale setting in [28,40], by considering two subpopulations of tumor cells interacting mutually and with the surrounding tissue. According to the go-or-grow hypothesis, these subpopulations consist of moving and proliferating cells, respectively. The mathematical setting also accommodates the effects of some therapy approaches. We prove the global existence of weak solutions to this model and perform numerical simulations to illustrate its behavior for different therapy strategies.

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Author:Christian Stinner, Christina Surulescu, Aydar Uatay
Document Type:Preprint
Language of publication:English
Publication Date:2016/01/29
Year of Publication:2016
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2016/02/01
Tag:asymptotic behavior; delay; go-or-grow; haptotaxis; multiscale model; tumor cell invasion
Number of page:32
Source:Mathematical Models and Methods in Applied Sciences 26, No. 11, 2163-2201 (2016).
Faculties / Organisational entities:Kaiserslautern - Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B40 Asymptotic behavior of solutions
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 / 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