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Convergence of the Allen-Cahn Equation to multi-phase mean-curvature flow
Tim Bastian Laux and Thilo Martin SimonAbstract
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.
- Received:
- 23.06.16
- Published:
- 28.06.16
- MSC Codes:
- 35A15, 35K57, 35K93
- Keywords:
- mean curvature flow, Allen-Cahn equation