Global existence of classical solutions and numerical simulations of a cancer invasion model

authored by

Mario Fuest, Shahin Heydari, Petr Knobloch, Johannes Lankeit, Thomas Wick

Abstract

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.

Organisation(s)

Institute of Applied Mathematics

External Organisation(s)

Charles University

Type

Article

Journal

ESAIM: Mathematical Modelling and Numerical Analysis

Volume

57

Pages

1893-1919

No. of pages

27

ISSN

2822-7840

Publication date

03.07.2023

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Analysis, Numerical Analysis, Modelling and Simulation, Computational Mathematics, Applied Mathematics

Sustainable Development Goals

SDG 3 - Good Health and Well-being

Electronic version(s)

https://doi.org/10.48550/arXiv.2205.08168 (Access: Open)
https://doi.org/10.1051/m2an/2023037 (Access: Open)