Nonlocal diffusion of smooth sets

Mathematics in Engineering

Anoumou Attiogbe¹  Mouhamed Moustapha Fall¹  El Hadji Abdoulaye Thiam² 

[1] 1. African Institute for Mathematical Sciences in Senegal, KM 2, Route de Joal, B.P. 14 18. Mbour, Senegal;2. Université Iba Der Thiam de Thies, UFR des Sciences et Techniques, département de mathématiques, Thies;

关键词: motion by fractional mean curvature flow;    fractional heat equation;    fractional mean curvature;    harmonic extension;   

DOI  :  10.3934/mine.2022009

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown