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MiS Preprint
37/2016
Convergence of the Allen-Cahn Equation to multi-phase mean-curvature flow
Tim Bastian Laux and Thilo Martin Simon
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 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.
