On the evolutionary dynamics of the cahn-hilliard equation with cut-off mass source

Chaeyoung Lee, Hyundong Kim, Sungha Yoon, Jintae Park, Sangkwon Kim, Junxiang Yang, Junseok Kim

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)242-260
Number of pages19
JournalNumerical Mathematics
Volume14
Issue number1
DOIs
Publication statusPublished - 2020 Oct

Keywords

  • Cahn-Hilliard equation
  • Finite difference method
  • Logistic source
  • Tumor growth application

ASJC Scopus subject areas

  • Modelling and Simulation
  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'On the evolutionary dynamics of the cahn-hilliard equation with cut-off mass source'. Together they form a unique fingerprint.

Cite this