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Mean curvature flow by the Allen–Cahn equation

Published online by Cambridge University Press:  13 May 2015

D. S. LEE  and
J. S. KIM
D. S. LEE
Affiliation:
Department of Mathematical Sciences, Ulsan National Institute of Science and Technology, Ulsan 689-798, Republic of Korea
J. S. KIM
Affiliation:
Department of Mathematics, Korea University, Seoul 136-713, Republic of Korea email: esen@unist.ac.kr, cfdkim@korea.ac.kr
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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.

Keywords

motion by mean curvatureAllen-Cahn equationcontact angle condition

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Type
Papers
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European Journal of Applied Mathematics , Volume 26 , Issue 4 , August 2015 , pp. 535 - 559
Copyright
Copyright © Cambridge University Press 2015 

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