Tumor growth with nutrients: stability of the tumor patches

TL;DR

This paper investigates the stability of tumor patches in a nutrient-driven growth model, showing that as nutrient diffusion decreases, the tumor boundary remains close to the smooth boundary observed at zero diffusion, indicating stability.

Contribution

It provides a mathematical analysis of tumor boundary stability under varying nutrient diffusion, highlighting boundary regularity as diffusion diminishes.

Findings

Tumor patch boundary remains close to the zero-diffusion boundary for small positive diffusion.

The boundary regularity persists uniformly as nutrient diffusion approaches zero.

The model demonstrates stability of tumor patches under nutrient diffusion variations.

Abstract

In this paper, we study a tumor growth model with nutrients. The contact inhibition for the tumor cells, presented in the model, results in the evolution of a congested tumor patch. We study the regularity of the tumor patch as the nutrients' diffusion strength $D$ diminishes. In particular, we show that for small $D>0$ the boundary of the tumor patch stays in a small neighborhood of the smooth tumor patch boundary obtained with $D=0$, uniformly with respect to the Hausdorff distance.