Contents Online
Communications in Mathematical Sciences
Volume 17 (2019)
Number 6
Sharp interface limit of a diffuse interface model for tumor-growth
Pages: 1557 – 1593
DOI: https://dx.doi.org/10.4310/CMS.2019.v17.n6.a4
Authors
Abstract
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.
Keywords
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