Existence result and free boundary limit of a tumor growth model with necrotic core

TL;DR

This paper proves the existence of solutions and analyzes the free boundary limit in a tumor growth model with complex diffusion effects, providing insights into tumor evolution and mathematical properties of the model.

Contribution

It establishes global existence of weak solutions and rigorously justifies the free boundary limit for a tumor growth model with nonlinear diffusion effects.

Findings

Proved global existence of weak solutions.

Justified convergence to Hele-Shaw type free boundary problem.

Analyzed convergence rate in L^1 spaces.

Abstract

We analyze a system of cross-diffusion equations that models the growth of an avascular-tumor spheroid. The model incorporates two nonlinear diffusion effects, degeneracy type and super diffusion. We prove the global existence of weak solutions and justify the convergence towards the free boundary problem of the Hele-Shaw type when the pressure gets stiff. We also investigate the convergence rate of the solutions in $L^1-$Lebesgue spaces.