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

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

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

Organisationseinheiten

Externe Organisationen

  • Charles University
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Seiten (von - bis)1893-1919
Seitenumfang27
FachzeitschriftESAIM: Mathematical Modelling and Numerical Analysis
Jahrgang57
Ausgabenummer4
PublikationsstatusVeröffentlicht - 3 Juli 2023

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.

ASJC Scopus Sachgebiete

Ziele für nachhaltige Entwicklung

Zitieren

Global existence of classical solutions and numerical simulations of a cancer invasion model. / Fuest, Mario; Heydari, Shahin; Knobloch, Petr et al.
in: ESAIM: Mathematical Modelling and Numerical Analysis, Jahrgang 57, Nr. 4, 03.07.2023, S. 1893-1919.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Fuest, Mario ; Heydari, Shahin ; Knobloch, Petr et al. / Global existence of classical solutions and numerical simulations of a cancer invasion model. in: ESAIM: Mathematical Modelling and Numerical Analysis. 2023 ; Jahrgang 57, Nr. 4. S. 1893-1919.
Download
@article{8d9f9a70e99c463fb946352d63363ed0,
title = "Global existence of classical solutions and numerical simulations of a cancer invasion model",
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.",
keywords = "Fixed-point scheme, Global existence, Haptotaxis, Numerical simulations, Tumour invasion",
author = "Mario Fuest and Shahin Heydari and Petr Knobloch and Johannes Lankeit and Thomas Wick",
year = "2023",
month = jul,
day = "3",
doi = "10.1051/m2an/2023037",
language = "English",
volume = "57",
pages = "1893--1919",
journal = "ESAIM: Mathematical Modelling and Numerical Analysis",
issn = "2822-7840",
publisher = "EDP Sciences",
number = "4",

}

Download

TY - JOUR

T1 - Global existence of classical solutions and numerical simulations of a cancer invasion model

AU - Fuest, Mario

AU - Heydari, Shahin

AU - Knobloch, Petr

AU - Lankeit, Johannes

AU - Wick, Thomas

PY - 2023/7/3

Y1 - 2023/7/3

N2 - 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.

AB - 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.

KW - Fixed-point scheme

KW - Global existence

KW - Haptotaxis

KW - Numerical simulations

KW - Tumour invasion

UR - http://www.scopus.com/inward/record.url?scp=85164539710&partnerID=8YFLogxK

U2 - 10.1051/m2an/2023037

DO - 10.1051/m2an/2023037

M3 - Article

AN - SCOPUS:85164539710

VL - 57

SP - 1893

EP - 1919

JO - ESAIM: Mathematical Modelling and Numerical Analysis

JF - ESAIM: Mathematical Modelling and Numerical Analysis

SN - 2822-7840

IS - 4

ER -

Von denselben Autoren