Calculus of Variations and Geometric Measure Theory

S. Dipierro - M. Novaga - E. Valdinoci

Time-fractional Allen-Cahn equations versus powers of the mean curvature

created by novaga on 09 Feb 2024

[BibTeX]

Submitted Paper

Inserted: 9 feb 2024

Year: 2024

ArXiv: 2402.05250 PDF

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.