Well-posedness and stability analysis for a moving boundary problem modelling the growth of nonnecrotic tumors

TL;DR

This paper analyzes a moving boundary model for nonnecrotic tumor growth, establishing well-posedness and stability of radially symmetric solutions using abstract evolution equations and linear stability analysis.

Contribution

It introduces a novel mathematical framework for tumor growth modeling, proving local well-posedness and stability properties of equilibrium states.

Findings

Proved local well-posedness in small Hölder spaces.

Characterized stability of radially symmetric tumor solutions.

Established conditions for stability based on linearized analysis.

Abstract

We study a moving boundary problem describing the growth of nonnecrotic tumors in different regimes of vascularisation. This model consists of two decoupled Dirichlet problem, one for the rate at which nutrient is added to the tumor domain and one for the pressure inside the tumor. These variables are coupled by a relation which describes the dynamic of the boundary. By re-expressing the problem as an abstract evolution equation, we prove local well-posedness in the small Hoelder spaces context. Further on, we use the principle of linearised stability to characterise the stability properties of the unique radially symmetric equilibrium of the problem.