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MiS Preprint

Convergence of the Allen-Cahn Equation to multi-phase mean-curvature flow

Tim Bastian Laux and Thilo Martin Simon


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 multi-phase 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.

Jun 23, 2016
Jun 28, 2016
MSC Codes:
35A15, 35K57, 35K93
mean curvature flow, Allen-Cahn equation

Related publications

2018 Repository Open Access
Tim Bastian Laux and Thilo Martin Simon

Convergence of the Allen-Cahn equation to multiphase mean curvature flow

In: Communications on pure and applied mathematics, 71 (2018) 8, pp. 1597-1647