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

2016/05/30 by Anna Zhigun, Zhigun, Anna, Christina Surulescu +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #35B45 #35D30 #35K20 #35K51 #35K57 #35K59 #35K65 #35Q92 #92C17 #Analysis of PDEs (math.AP) #Evolution and Genetic Dynamics #FOS: Mathematics #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth #Microtubule and mitosis dynamics

paper · pdf · doi:10.48550/arxiv.1605.09226

openalex publication_date 2016/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose and study a strongly coupled PDE-ODE-ODE system modeling cancer\ncell invasion through a tissue network under the go-or-grow hypothesis\nasserting that cancer cells can either move or proliferate. Hence our setting\nfeatures two interacting cell populations with their mutual transitions and\ninvolves tissue-dependent degenerate diffusion and haptotaxis for the moving\nsubpopulation. The proliferating cells and the tissue evolution are\ncharacterized by way of ODEs for the respective densities. We prove the global\nexistence of weak solutions and illustrate the model behaviour by numerical\nsimulations in a two-dimensional setting.\n

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