Serena Dipierro, Matteo Novaga, Enrico Valdinoci
Published 2024-02-07Version 1
We show by a formal asymptotic expansion that level sets of solutions of a time-fractional Allen-Cahn equation evolve by a geometric flow whose normal velocity is a positive power of the mean curvature. This connection is quite intriguing, since the original equation is nonlocal and the evolution of its solutions depends on all previous states, but the associated geometric flow is of purely local type, with no memory effect involved.
On representation of boundary integrals involving the mean curvature for mean-convex domains
Nondegeneracy of critical points of the mean curvature of the boundary for Riemannian manifolds
Equivalence between a time-fractional and an integer-order gradient flow: The memory effect reflected in the energy
![QR code for arXiv:2402.05250 [math.AP]](http://oss.arxitics.com/images/favicon.svg)