Convergence of the Nonlocal Allen–Cahn Equation to Mean Curvature Flow

URN to cite this document:: urn:nbn:de:bvb:355-epub-781115
DOI to cite this document:: 10.5283/epub.78111

Abels, Helmut

; Hurm, Christoph

; Moser, Maximilian

License: Creative Commons Attribution Non-commercial 4.0
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Date of publication of this fulltext: 07 Nov 2025 09:31

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Abstract

We prove convergence of the nonlocal Allen–Cahn equation to mean curvature flow in the sharp interface limit, in the situation when the parameter corresponding to the kernel goes to zero fast enough with respect to the diffuse interface thickness. The analysis is done in the case of a -kernel, under periodic boundary conditions and in both two and three space dimensions. We use the approximate ...