TY - JOUR
AB - 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.
AU - Fischer, Julian L
AU - Laux, Tim
AU - Simon, Theresa M.
ID - 9039
IS - 6
JF - SIAM Journal on Mathematical Analysis
SN - 00361410
TI - Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies
VL - 52
ER -