Portal de Periódicos da CAPES

Convergence Rates of the Allen--Cahn Equation to Mean Curvature Flow: A Short Proof Based on Relative Entropies

2020; Society for Industrial and Applied Mathematics; Volume: 52; Issue: 6 Linguagem: Inglês

10.1137/20m1322182

1095-7154

Julian Fischer, Tim Laux, Theresa M. Simon,

Geometric Analysis and Curvature Flows

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.