Method of the distance function to the Bence-Merriman-Osher algorithm for motion by mean curvature

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2005, 4(2): 311-339. doi: 10.3934/cpaa.2005.4.311

Method of the distance function to the Bence-Merriman-Osher algorithm for motion by mean curvature

Y. Goto ^1, , K. Ishii ^2, and T. Ogawa ^3,

1.	NTT Comware, Minato, Tokyo, 108-8019, Japan
2.	Faculty of Maritime Sciences, Kobe University, Higashinada, Kobe 658-0022, Japan
3.	Mathematical Institute, Tohoku University, Aoba, Sendai 980-8578, Japan

Received March 2003 Revised May 2004 Published March 2005

Abstract
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A new proof of the convergence of the Bence-Merriman-Osher algorithm for the motion of mean curvature is given. The idea is making use of the approximate distance function to the interface and analogous argument in the singular limiting problem for the Allen-Cahn equation via an auxiliary function given by the primitive function of the heat kernel.

Keywords: signed distance function, Motionby mean curvature, viscosity solutions., Bence-Merrina-Osher algorithm.

Mathematics Subject Classification: 35K65,35K55,65M99.

Citation: Y. Goto, K. Ishii, T. Ogawa. Method of the distance function to the Bence-Merriman-Osher algorithm for motion by mean curvature. Communications on Pure & Applied Analysis, 2005, 4 (2) : 311-339. doi: 10.3934/cpaa.2005.4.311

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