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.
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页码：571 / 590
页数：20
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