Work

Global classical solutions for a metastatic cancer invasion model with negative haptotaxis

Year: 2026

Type: preprint

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 $L^p$-estimates. Numerical simulations illustrate primary tumor invasion and metastatic spread to secondary sites.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.01268

Authors: Mohan, Nishith, Katsaounis, Dimitrios

Institutions: University of Kaiserslautern, Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau, RWTH Aachen University

Language: English

Topic: Mathematical Biology Tumor Growth

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

SDG: Good health and well-being

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, Universität Paderborn