Varifold solutions of a sharp interface limit of a diffuse interface model for tumor growth

Abstract

We discuss the sharp interface limit of a diffuse interface model for a coupled Cahn–Hilliard–Darcy system that models tumor growth when a certain parameter $ϵ>0$, related to the interface thickness, tends to zero. In particular, we prove that weak solutions to the related initial boundary value problem tend to varifold solutions of a corresponding sharp interface model when $ϵ$ goes to zero.