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

PDF Abstract
No code implementations yet. Submit your code now


Analysis of PDEs