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

Takashi Kagaya

doi:10.1007/s00208-018-1720-x

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

Takashi Kagaya

基礎理論研究部門

研究成果: Contribution to journal › Article

抜粋

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.

元の言語	英語
ページ（範囲）	1485-1528
ページ数	44
ジャーナル	Mathematische Annalen
巻	373
発行部数	3-4
DOI	https://doi.org/10.1007/s00208-018-1720-x
出版物ステータス	出版済み - 4 1 2019

All Science Journal Classification (ASJC) codes

Mathematics(all)

文献にアクセス

10.1007/s00208-018-1720-x

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これを引用

Kagaya, T. (2019). Convergence of the Allen–Cahn equation with a zero Neumann boundary condition on non-convex domains. Mathematische Annalen, 373(3-4), 1485-1528. https://doi.org/10.1007/s00208-018-1720-x

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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{\textquoteright}s mean curvature flow with a generalized right angle condition on the boundary of the domain.",

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