Communications in Mathematical Sciences

Volume 17 (2019)

Number 6

Sharp interface limit of a diffuse interface model for tumor-growth

Pages: 1557 – 1593



Mingwen Fei (School of Mathematics and Statistics Sciences, Anhui Normal University, Wuhu, China)

Tao Tao (School of Mathematical Sciences, Shandong University, Jinan, China)

Wei Wang (Department of Mathematics, Zhejiang University, Hangzhou, China)


We consider the asymptotic limit of a diffuse interface model for tumor-growth when a parameter $\varepsilon$ proportional to the thickness of the diffuse interface goes to zero. An approximate solution which shows explicitly the behavior of the true solution for small $\varepsilon$ will be constructed by using the matched expansion method. Based on the energy method, and a spectral condition in particular, we establish a smallness estimate of the difference between the approximate solution and the true solution.


sharp interface limit, spectral condition, matched asymptotic expansion

2010 Mathematics Subject Classification

35Q30, 76D03

Received 9 July 2018

Accepted 1 July 2019

Published 26 December 2019