Analysis of a Mixture Model of Tumor Growth

TL;DR

This paper investigates a coupled Cahn-Hilliard-Hele-Shaw model for tumor growth, establishing existence, uniqueness, regularity, and exponential convergence of solutions in 2D and 3D for large initial data.

Contribution

It provides the first rigorous analysis of strong solutions for this tumor growth model, including regularity results and long-term behavior in both two and three dimensions.

Findings

Global existence and uniqueness of solutions in 2D and 3D.

Solutions exhibit higher order spatial and Gevrey regularity.

Solutions converge exponentially to a constant state over time.

Abstract

We study an initial-boundary value problem (IBVP) for a coupled Cahn-Hilliard-Hele-Shaw system that models tumor growth. For large initial data with finite energy, we prove global (local resp.) existence, uniqueness, higher order spatial regularity and Gevrey spatial regularity of strong solutions to the IBVP in 2D (3D resp.). Asymptotically in time, we show that the solution converges to a constant state exponentially fast as time tends to infinity under certain assumptions.