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

被引：14

作者：

Melchionna, Stefano ^{[1
]}

Rocca, Elisabetta ^{[2
,3
]}

机构：

[1] Univ Vienna, Fac Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

[2] Univ Pavia, Dipartimento Matemat, Via Ferrata 5, I-27100 Pavia, Italy

[3] CNR, IMATI, Via Ferrata 5, I-27100 Pavia, Italy

来源：

INTERFACES AND FREE BOUNDARIES | 2017年 / 19卷 / 04期

基金：

奥地利科学基金会;

关键词：

Free boundary problems; diffuse interface models; sharp interface limit; Cahn-Hilliard equation; Darcy law; tumor growth; CAHN-HILLIARD EQUATION; MIXTURE MODEL;

D O I：

10.4171/IFB/393

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 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 epsilon goes to zero.

引用

页码：571 / 590

页数：20

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