@Article{NMTMA-14-1,
author = {Yoon, Sungha and Lee, Chaeyoung and Kim, Hyundong and Park, Jintae and Yoon, Sungha and Sangkwon, Kim and Yang, Junxiang and Park, Jintae and Kim, Junseok and Sangkwon, Kim and Yang, 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 = {2021},
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 = {https://global-sci.com/article/90297/on-the-evolutionary-dynamics-of-the-cahn-hilliard-equation-with-cut-off-mass-source}
}