Bifurcation analysis for a free boundary problem modeling tumor growth

TL;DR

This paper analyzes a free boundary model of tumor growth, demonstrating the existence of non-radially symmetric stationary solutions through bifurcation analysis, simplifying the tumor as an incompressible fluid without chemical inhibitors.

Contribution

It introduces a bifurcation approach to identify non-radial stationary solutions in a tumor growth model expressed as an operator equation.

Findings

Existence of non-radially symmetric stationary solutions

Reformulation of the tumor model as an operator equation

Application of bifurcation theory to tumor growth modeling

Abstract

In this paper we deal with a free boundary problem modeling the growth of nonnecrotic tumors.The tumor is treated as an incompressible fluid, the tissue elasticity is neglected and no chemical inhibitor species are present. We re-express the mathematical model as an operator equation and by using a bifurcation argument we prove that there exist stationary solutions of the problem which are not radially symmetric.