On the Evolutionary Dynamics of the Cahn-Hilliard Equation with Cut-Off Mass Source
Year: 2021
Author: Sungha Yoon, Chaeyoung Lee, Hyundong Kim, Jintae Park, Sungha Yoon, Sangkwon Kim, Junxiang Yang, Jintae Park, Junseok Kim, Sangkwon Kim, Junxiang Yang, Junseok Kim
Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 1 : pp. 242–260
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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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2020-0051
Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 1 : pp. 242–260
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Cahn-Hilliard equation logistic source finite difference method tumor growth application.
Author Details
Sungha Yoon Email
Chaeyoung Lee Email
Hyundong Kim Email
Jintae Park Email
Sungha Yoon Email
Sangkwon Kim Email
Junxiang Yang Email
Jintae Park Email
Junseok Kim Email
Sangkwon Kim Email
Junxiang Yang Email
Junseok Kim Email
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