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

verfasst von

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.

Organisationseinheit(en)

Institut für Angewandte Mathematik

Externe Organisation(en)

Charles University

Typ

Artikel

Journal

ESAIM: Mathematical Modelling and Numerical Analysis

Band

57

Seiten

1893-1919

Anzahl der Seiten

27

ISSN

2822-7840

Publikationsdatum

03.07.2023

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Analysis, Numerische Mathematik, Modellierung und Simulation, Computational Mathematics, Angewandte Mathematik

Ziele für nachhaltige Entwicklung

SDG 3 – Gute Gesundheit und Wohlergehen

Elektronische Version(en)

https://doi.org/10.48550/arXiv.2205.08168 (Zugang: Offen)
https://doi.org/10.1051/m2an/2023037 (Zugang: Offen)