A new asymptotic model of multilayer tumor growth

TL;DR

This paper introduces a novel weakly nonlinear asymptotic model for multilayer tumor growth, capturing complex dynamics through a high-order PDE system and analyzing interface collision phenomena.

Contribution

It develops a new asymptotic PDE model for multilayer tumor growth and investigates its well-posedness near interface collision scenarios.

Findings

Derivation of a nonlinear, nonlocal high-order PDE system

Analysis of model well-posedness during interface collision

Insights into tumor growth dynamics from asymptotic modeling

Abstract

In this paper we study the growth of a tumor colony of multilayer type and focus on how the tumor grows from a near flat (when compared to the length of the tumor as, for instance, in the case of a bone tumor in a femur) initial colony. In particular we derive and study a new weakly nonlinear asymptotic model of multilayer tumor growth. The model takes the form of a nonlinear and nonlocal high order system of PDEs. Finally, motivated by the possibility of a finite time collision of the interfaces, we study the well-posedness of this system.