A note on a multi-layer tumor growth model

TL;DR

This paper revisits a multi-layer tumor growth model, extending previous work by removing periodic boundary conditions and showing that stationary solutions remain unchanged, thereby enhancing the model's realism.

Contribution

It generalizes the existing tumor growth model by eliminating periodic boundary conditions, maintaining the same stationary solutions, and improving its applicability to realistic scenarios.

Findings

Stationary solutions are preserved without periodic boundary conditions.

The generalized model remains well-posed and stable.

Enhanced realism in tumor growth modeling.

Abstract

A two-dimensional free boundary model for the growth of multi-layer tumors has been proposed in [S. Cui, J. Escher: ARMA 191 (2009) 173-193] where the authors derive well-posedness in a functional analytic setting, the stationary solutions and their asymptotic stability. In this note, we consider once again the cancer growth model of [S. Cui, J. Escher: ARMA 191 (2009) 173-193] but coping without periodic boundary conditions for the $x$ variable which is reasonable from the point of view of modeling. The paper points out that the generalized model allows for the same stationary solutions as compared to the model with periodic boundary conditions.