Analysis of a mathematical model describing necrotic tumor growth

TL;DR

This paper investigates a mathematical model of necrotic tumor growth, analyzing stationary solutions and the evolution of tumor boundaries, with a focus on well-posedness in radially symmetric cases.

Contribution

It characterizes all radially symmetric stationary solutions and reduces the tumor growth model to a nonlinear evolution problem, establishing local well-posedness.

Findings

All radially symmetric stationary solutions identified

Model reduced to a nonlinear evolution equation

Local well-posedness proven for small initial data

Abstract

In this paper we study a model describing the growth of necrotic tumors in different regimes of vascularisation. The tumor consists of a necrotic core of death cells and a surrounding nonnecrotic shell. The corresponding mathematical formulation is a moving boundary problem where both boundaries delimiting the nonnecrotic shell are allowed to evolve in time.We determine all radially symmetric stationary solutions of the problem and reduce the moving boundary problem into a nonlinear evolution. Parabolic theory provides us the perfect context in order to show local well-posed of the problem for small initial data.