Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies

18 Aug 2020  ·  Fischer Julian, Laux Tim, Simon Theresa M. ·

We give a short and self-contained proof for rates of convergence of the Allen-Cahn equation towards mean curvature flow, assuming that a classical (smooth) solution to the latter exists and starting from well-prepared initial data. Our approach is based on a relative entropy technique... In particular, it does not require a stability analysis for the linearized Allen-Cahn operator. As our analysis also does not rely on the comparison principle, we expect it to be applicable to more complex equations and systems. read more

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Analysis of PDEs