Existence and uniqueness of global classical solutions to a two species cancer invasion haptotaxis model

We consider a haptotaxis cancer invasion model that includes two families of cancer cells. Both families, migrate on the extracellular matrix and proliferate. Moreover the model describes an epithelial-to-mesenchymal-like transition between the two families, as well as a degradation and a self-recon...

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Bibliographic Details
Published in:arXiv.org 2017-04
Main Authors: Giesselmann, Jan, Kolbe, Niklas, Lukacova-Medvidova, Maria, Sfakianakis, Nikolaos
Format: Article
Language:English
Subjects:
Cancer
Extracellular matrix
Uniqueness
Online Access:Get full text
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Summary:We consider a haptotaxis cancer invasion model that includes two families of cancer cells. Both families, migrate on the extracellular matrix and proliferate. Moreover the model describes an epithelial-to-mesenchymal-like transition between the two families, as well as a degradation and a self-reconstruction process of the extracellular matrix. We prove positivity and conditional global existence and uniqueness of the classical solutions of the problem for large initial data.
ISSN:2331-8422
DOI:10.48550/arxiv.1704.08208