Convergence of the Allen-Cahn Equation to Multiphase Mean Curvature Flow

Document Type

Article

Publication Date

8-1-2018

Abstract

We present a convergence result for solutions of the vector-valued Allen-Cahn equation. In the spirit of the work of Luckhaus and Sturzenhecker we establish convergence towards a distributional formulation of multiphase mean~curvature flow using sets of finite perimeter. Like their result, ours relies on the assumption that the time-integrated energies of the approximations converge to those of the limit. Furthermore, we apply our proof to two variants of the equation, incorporating external forces and volume constraints.© 2018 Wiley Periodicals, Inc.

Identifier

85044750947 (Scopus)

Publication Title

Communications on Pure and Applied Mathematics

External Full Text Location

https://doi.org/10.1002/cpa.21747

e-ISSN

10970312

ISSN

00103640

First Page

1597

Last Page

1647

Issue

8

Volume

71

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