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.
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