| Issue |
ESAIM: M2AN
Volume 57, Number 4, July-August 2023
|
|
|---|---|---|
| Page(s) | 1893 - 1919 | |
| DOI | https://doi.org/10.1051/m2an/2023037 | |
| Published online | 03 July 2023 | |
Global existence of classical solutions and numerical simulations of a cancer invasion model
1
Leibniz University Hannover, Institute of Applied Mathematics, Welfengarten 1, 30167 Hannover, Germany
2
Charles University, Faculty of Mathematics and Physics, Sokolovská 83, 18675 Praha 8, Czech Republic
* Corresponding author: fuest@ifam.uni-hannover.de
Received:
17
May
2022
Accepted:
28
April
2023
In this paper, we study a cancer invasion model both theoretically and numerically. The model is a nonstationary, nonlinear system of three coupled partial differential equations modeling the motion of cancer cells, degradation of the extracellular matrix, and certain enzymes. We first establish existence of global classical solutions in both two- and three-dimensional bounded domains, despite the lack of diffusion of the matrix-degrading enzymes and corresponding regularizing effects in the analytical treatment. Next, we give a weak formulation and apply finite differences in time and a Galerkin finite element scheme for spatial discretization. The overall algorithm is based on a fixed-point iteration scheme. Our theory and numerical developments are accompanied by some simulations in two and three spatial dimensions.
Mathematics Subject Classification: 35A01 / 35K57 / 35Q92 / 65M22 / 65M60 / 92C17
Key words: Haptotaxis / Tumour invasion / Global existence / Fixed-point scheme / Numerical simulations
© The authors. Published by EDP Sciences, SMAI 2023
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