Tumor Growth with Nutrients: Regularity and Stability

TL;DR

This paper analyzes a tumor growth model with nutrients, demonstrating regularity and stability of tumor patches under specific conditions, contrasting with models involving nutrient diffusion or cell death.

Contribution

It provides new mathematical results on tumor patch regularity, contraction estimates, and convergence rates in a nutrient-limited tumor growth model.

Findings

Tumor density exhibits regularizing dynamics without nutrient diffusion or cell death.

The model shows exponential convergence to a stable tumor shape.

Boundary regularity of tumor patches is established under the specified conditions.

Abstract

In this paper we study a tumor growth model with nutrients. The model presents dynamic patch solutions due to the contact inhibition among the tumor cells. We show that when the nutrients do not diffuse and the cells do not die, the tumor density exhibits regularizing dynamics. In particular, we provide contraction estimates, exponential rate of asymptotic convergence, and boundary regularity of the tumor patch. These results are in sharp contrast to the models either with nutrient diffusion or with death rate in tumor cells.