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September/October 2017 Convergence of the Allen-Cahn equation with constraint to Brakke's mean curvature flow
Keisuke Takasao
Adv. Differential Equations 22(9/10): 765-792 (September/October 2017).

Abstract

In this paper, we consider the Allen-Cahn equation with constraint. In 1994, Chen and Elliott [9] studied the asymptotic behavior of the solution of the Allen-Cahn equation with constraint. They proved that the zero level set of the solution converges to the classical solution of the mean curvature flow under the suitable conditions on initial data. In 1993, Ilmanen [20] proved the existence of the mean curvature flow via the Allen-Cahn equation without constraint in the sense of Brakke. We proved the same conclusion for the Allen-Cahn equation with constraint.

Citation

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Keisuke Takasao. "Convergence of the Allen-Cahn equation with constraint to Brakke's mean curvature flow." Adv. Differential Equations 22 (9/10) 765 - 792, September/October 2017.

Information

Published: September/October 2017
First available in Project Euclid: 27 May 2017

zbMATH: 06780899
MathSciNet: MR3656492

Subjects:
Primary: 35K57, 53C44

Rights: Copyright © 2017 Khayyam Publishing, Inc.

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Vol.22 • No. 9/10 • September/October 2017
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