Author
Colson, C
Sanchez-Garduno, F
Byrne, H
Maini, P
Lorenzi, T
Journal title
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
DOI
10.1098/rspa.2021.0593
Issue
2256
Volume
477
Last updated
2024-03-25T15:41:10.01+00:00
Abstract
In this paper, we carry out a travelling-wave analysis of a model of tumour invasion with degenerate, cross-dependent diffusion. We consider two types of invasive fronts of tumour tissue into extracellular matrix (ECM), which represents healthy tissue. These types differ according to whether the density of ECM far ahead of the wave front is maximal or not. In the former case, we use a shooting argument to prove that there exists a unique travelling wave solution for any positive propagation speed. In the latter case, we further develop this argument to prove that there exists a unique travelling wave solution for any propagation speed greater than or equal to a strictly positive minimal wave speed. Using a combination of
analytical and numerical results, we conjecture that the minimal wave speed depends monotonically on the degradation rate of ECM by tumour cells and the ECM density far ahead of the front.
Symplectic ID
1210645
Favourite
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Publication type
Journal Article
Publication date
15 Dec 2021
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