Nonsymmetric traveling wave solution to a Hele-Shaw type tumor growth model

TL;DR

This paper proves the existence of nonsymmetric traveling wave solutions in a Hele-Shaw tumor growth model, highlighting intrinsic boundary instability in tumor dynamics within a two-dimensional domain.

Contribution

It introduces the first proof of nonsymmetric traveling wave solutions in a Hele-Shaw tumor model, extending understanding of boundary instability phenomena.

Findings

Existence of nonsymmetric traveling wave solutions

Boundary instability is intrinsic to tumor growth dynamics

Model derived from porous medium equations in incompressible limit

Abstract

We consider a Hele-Shaw model that describes tumor growth subject to nutrient supply. The model is derived by taking the incompressible limit of porous medium type equations, and the boundary instability of this model was recently studied in \cite{feng2022tumor} using asymptotic analysis. In this paper, we further prove the existence of nonsymmetric traveling wave solutions to the model in a two dimensional tube-like domain, which reflect intrinsic boundary instability in tumor growth dynamics.