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...
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| Published in | Mathematics in engineering Vol. 4; no. 2; pp. 1 - 22 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
AIMS Press
2021
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| Subjects | |
| Online Access | Get full text |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Fall, Mouhamed Moustapha Attiogbe, Anoumou Thiam, El Hadji Abdoulaye |
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| Title | Nonlocal diffusion of smooth sets |
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