Mean curvature flow by the Allen-Cahn equation

D. S. Lee; J. S. Kim

doi:10.1017/S0956792515000200

Mean curvature flow by the Allen-Cahn equation

D. S. Lee, J. S. Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

22 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 language	English
Pages (from-to)	535-559
Number of pages	25
Journal	European Journal of Applied Mathematics
Volume	26
Issue number	4
DOIs	https://doi.org/10.1017/S0956792515000200
Publication status	Published - 2015 Aug 24

Bibliographical note

Publisher Copyright:
Copyright © Cambridge University Press 2015.

Keywords

Allen-Cahn equation
contact angle condition
motion by mean curvature

ASJC Scopus subject areas

Applied Mathematics

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10.1017/S0956792515000200

Cite this

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AB - 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.

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KW - contact angle condition

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Mean curvature flow by the Allen-Cahn equation

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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