On the Evolutionary Dynamics of the Cahn-Hilliard Equation with Cut-Off Mass Source
- Authors
- Lee, Chaeyoung; Kim, Hyundong; Yoon, Sungha; Park, Jintae; Kim, Sangkwon; Yang, Junxiang; Kim, Junseok
- Issue Date
- 2월-2021
- Publisher
- GLOBAL SCIENCE PRESS
- Keywords
- Cahn-Hilliard equation; logistic source; finite difference method; tumor growth application
- Citation
- NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, v.14, no.1, pp.242 - 260
- Indexed
- SCIE
SCOPUS
- Journal Title
- NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS
- Volume
- 14
- Number
- 1
- Start Page
- 242
- End Page
- 260
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/50012
- DOI
- 10.4208/nmtma.OA-2020-0051
- ISSN
- 1004-8979
- Abstract
- 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.
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Collections - College of Science > Department of Mathematics > 1. Journal Articles
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