Details
| Original language | English |
|---|---|
| Pages (from-to) | 1893-1919 |
| Number of pages | 27 |
| Journal | ESAIM: Mathematical Modelling and Numerical Analysis |
| Volume | 57 |
| Issue number | 4 |
| Publication status | Published - 3 Jul 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.
Keywords
- Fixed-point scheme, Global existence, Haptotaxis, Numerical simulations, Tumour invasion
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Numerical Analysis
- Mathematics(all)
- Modelling and Simulation
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
Sustainable Development Goals
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In: ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 57, No. 4, 03.07.2023, p. 1893-1919.
Research output: Contribution to journal › Article › Research › peer review
}
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 -