Convergence of nonlocal threshold dynamics approximations to front propagation

Details Convergence of nonlocal threshold dynamics approximations to front propagation Convergence of nonlocal threshold dynamics approximations to front propagation

2008-05-16

arxiv.org/abs/0805.2618v1

Mathematics

Analysis of PDEs

19 pages

Scientific paper

10.1007/s00205-008-0181-x

In this note we prove that appropriately scaled threshold dynamics-type algorithms corresponding to the fractional Laplacian of order $\alpha \in (0,2)$ converge to moving fronts. When $\alpha \geqq 1$ the resulting interface moves by weighted mean curvature, while for $\alpha <1$ the normal velocity is nonlocal of ``fractional-type.'' The results easily extend to general nonlocal anisotropic threshold dynamics schemes.

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