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

  • Stefano Melchionna

    Universität Wien, Austria
  • Elisabetta Rocca

    Università degli Studi di Pavia, Italy
Varifold solutions of a sharp interface limit of a diffuse interface model for tumor growth cover
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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\epsilon > 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\epsilon goes to zero.

Cite this article

Stefano Melchionna, Elisabetta Rocca, Varifold solutions of a sharp interface limit of a diffuse interface model for tumor growth. Interfaces Free Bound. 19 (2017), no. 4, pp. 571–590

DOI 10.4171/IFB/393