Global classical solutions for a metastatic cancer invasion model with negative haptotaxis
Abstract
We analyze a coupled PDE-ODE model for metastatic cancer invasion involving epithelial-like and mesenchymal-like cancer cells, cancer-associated fibroblasts (CAFs), the transforming growth factor β, matrix-degrading metalloproteinases, and extracellular matrix reconstruction by CAFs. The model incorporates bidirectional phenotypic transitions between epithelial-like and mesenchymal-like cancer cells, cancer-cell haptotaxis, negative fibroblast haptotaxis, as well as cell-specific proliferation. Under explicit parameter restrictions, we establish global classical solvability for the full model in two dimensions using an energy-based approach, and for a three-dimensional variant with constant phenotypic transition rates using coupled Lp-estimates. Numerical simulations illustrate primary tumor invasion and metastatic spread to secondary sites.
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BibTeX
@misc{mohan2026global,
title = {{Global classical solutions for a metastatic cancer invasion model with negative haptotaxis}},
author = {Nishith Mohan and Dimitrios Katsaounis},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01268},
eprint = {2610.01268},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01268},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Global classical solutions for a metastatic cancer invasion model with negative haptotaxis
AU - Nishith Mohan
AU - Dimitrios Katsaounis
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01268
UR - https://arxiv.org/abs/2610.01268
AB - We analyze a coupled PDE-ODE model for metastatic cancer invasion involving epithelial-like and mesenchymal-like cancer cells, cancer-associated fibroblasts (CAFs), the transforming growth factor β, matrix-degrading metalloproteinases, and extracellular matrix reconstruction by CAFs. The model incorporates bidirectional phenotypic transitions between epithelial-like and mesenchymal-like cancer cells, cancer-cell haptotaxis, negative fibroblast haptotaxis, as well as cell-specific proliferation. Under explicit parameter restrictions, we establish global classical solvability for the full model in two dimensions using an energy-based approach, and for a three-dimensional variant with constant phenotypic transition rates using coupled L^p-estimates. Numerical simulations illustrate primary tumor invasion and metastatic spread to secondary sites.
ER -