Published Paper

Inserted: 9 feb 2024
Last Updated: 24 apr 2024

Journal: Physica D
Volume: 463
Number: Article 134172
Year: 2024

Abstract:

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.