Mean curvature flow by the Allen-Cahn equation

D. S. Lee, J. S. Kim

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)


In this paper, we investigate motion by mean curvature using the Allen-Cahn (AC) equation in two and three space dimensions. We use an unconditionally stable hybrid numerical scheme to solve the equation. Numerical experiments demonstrate that we can use the AC equation for applications to motion by mean curvature. We also study the curve-shortening flow with a prescribed contact angle condition.

Original languageEnglish
Pages (from-to)535-559
Number of pages25
JournalEuropean Journal of Applied Mathematics
Issue number4
Publication statusPublished - 2015 Aug 24

Bibliographical note

Publisher Copyright:
Copyright © Cambridge University Press 2015.


  • Allen-Cahn equation
  • contact angle condition
  • motion by mean curvature

ASJC Scopus subject areas

  • Applied Mathematics


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