Global existence for a degenerate haptotaxis model of cancer invasion

TL;DR

This paper introduces a complex PDE-ODE model for cancer invasion that incorporates tissue-dependent degenerate diffusion and haptotaxis, proving global solutions and demonstrating behavior through numerical simulations.

Contribution

It presents the first proof of global existence for a degenerate haptotaxis cancer invasion model with tissue-dependent diffusion.

Findings

Proved global existence of weak solutions.

Numerical simulations illustrate model behavior.

Model captures key features of cancer invasion.

Abstract

We propose and study a strongly coupled PDE-ODE system with tissue-dependent degenerate diffusion and haptotaxis that can serve as a model prototype for cancer cell invasion through the extracellular matrix. We prove the global existence of weak solutions and illustrate the model behaviour by numerical simulations for a two-dimensional setting.