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Convergence of the Allen–Cahn equation with a zero Neumann boundary condition on non-convex domains

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Abstract

We study a singular limit problem of the Allen–Cahn equation with a homogeneous Neumann boundary condition on non-convex domains with smooth boundaries under suitable assumptions for initial data. The main result is the convergence of the time parametrized family of the diffused surface energy to Brakke’s mean curvature flow with a generalized right angle condition on the boundary of the domain.

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Authors and Affiliations

  1. Institute of Mathematics for Industry, Kyushu University, Fukuoka, 819-0395, Japan

    Takashi Kagaya

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  1. Takashi Kagaya
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Correspondence to Takashi Kagaya.

Additional information

Communicated by Y. Giga.

The author is partially supported by JSPS Research Fellow Grant number 16J00547.

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Kagaya, T. Convergence of the Allen–Cahn equation with a zero Neumann boundary condition on non-convex domains. Math. Ann. 373, 1485–1528 (2019). https://doi.org/10.1007/s00208-018-1720-x

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  • DOI: https://doi.org/10.1007/s00208-018-1720-x

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