Mean curvature flow by the Allen-Cahn equation

D. S. Lee, Junseok Kim

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

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
Volume26
Issue number4
DOIs
Publication statusPublished - 2015 Aug 24

Fingerprint

Motion by Mean Curvature
Allen-Cahn Equation
Mean Curvature Flow
Contact angle
Unconditionally Stable
Contact Angle
Numerical Scheme
Experiments
Numerical Experiment
Curve
Demonstrate

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Mean curvature flow by the Allen-Cahn equation. / Lee, D. S.; Kim, Junseok.

In: European Journal of Applied Mathematics, Vol. 26, No. 4, 24.08.2015, p. 535-559.

Research output: Contribution to journalArticle

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