@Article{NMTMA-14-242,
author = {Lee , ChaeyoungKim , HyundongYoon , SunghaPark , JintaeKim , SangkwonYang , Junxiang and Kim , Junseok},
title = {On the Evolutionary Dynamics of the Cahn-Hilliard Equation with Cut-Off Mass Source},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2020},
volume = {14},
number = {1},
pages = {242--260},
abstract = {<p style="text-align: justify;">We investigate the effect of cut-off logistic source on evolutionary dynamics of a generalized Cahn-Hilliard (CH) equation in this paper. It is a well-known fact
that the maximum principle does not hold for the CH equation. Therefore, a generalized CH equation with logistic source may cause the negative concentration blow-up
problem in finite time. To overcome this drawback, we propose the cut-off logistic
source such that only the positive value greater than a given critical concentration
can grow. We consider the temporal profiles of numerical results in the one-, two-,
and three-dimensional spaces to examine the effect of extra mass source. Numerical
solutions are obtained using a finite difference multigrid solver. Moreover, we perform numerical tests for tumor growth simulation, which is a typical application of
generalized CH equations in biology. We apply the proposed cut-off logistic source
term and have good results.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2020-0051},
url = {http://global-sci.org/intro/article_detail/nmtma/18334.html}
}