Nonlocal diffusion of smooth sets

We consider normal velocity of smooth sets evolving by the $ s- $fractional diffusion. We prove that for small time, the normal velocity of such sets is nearly proportional to the mean curvature of the boundary of the initial set for $ s\in [\frac{1}{2}, 1) $ while, for $ s\in (0, \frac{1}{2}) $, it...

Full description

Saved in:
Bibliographic Details
Published inMathematics in engineering Vol. 4; no. 2; pp. 1 - 22
Main Authors Attiogbe, Anoumou, Fall, Mouhamed Moustapha, Thiam, El Hadji Abdoulaye
Format Journal Article
LanguageEnglish
Published AIMS Press 2021
Subjects
fractional heat equation
fractional mean curvature
harmonic extension
motion by fractional mean curvature flow
Online AccessGet full text

Cover

More Information
Summary:We consider normal velocity of smooth sets evolving by the $ s- $fractional diffusion. We prove that for small time, the normal velocity of such sets is nearly proportional to the mean curvature of the boundary of the initial set for $ s\in [\frac{1}{2}, 1) $ while, for $ s\in (0, \frac{1}{2}) $, it is nearly proportional to the fractional mean curvature of the initial set. Our results show that the motion by (fractional) mean curvature flow can be approximated by fractional heat diffusion and by a diffusion by means of harmonic extension of smooth sets.
ISSN:2640-3501
2640-3501
DOI:10.3934/mine.2022009