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

Takashi Kagaya

研究成果: ジャーナルへの寄稿 › 記事

抄録

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
出版物ステータス出版済み - 4 1 2019

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Allen-Cahn Equation
Neumann Boundary Conditions
Right angle
Mean Curvature Flow
Singular Limit
Surface Energy
Zero
Family

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

これを引用

Convergence of the Allen–Cahn equation with a zero Neumann boundary condition on non-convex domains. / Kagaya, Takashi.

：: Mathematische Annalen, 巻 373, 番号 3-4, 01.04.2019, p. 1485-1528.

研究成果: ジャーナルへの寄稿 › 記事

Kagaya, T 2019, 'Convergence of the Allen–Cahn equation with a zero Neumann boundary condition on non-convex domains', Mathematische Annalen, 巻. 373, 番号 3-4, pp. 1485-1528. https://doi.org/10.1007/s00208-018-1720-x
Kagaya T. Convergence of the Allen–Cahn equation with a zero Neumann boundary condition on non-convex domains. Mathematische Annalen. 2019 4 1;373(3-4):1485-1528. https://doi.org/10.1007/s00208-018-1720-x
Kagaya, Takashi. / Convergence of the Allen–Cahn equation with a zero Neumann boundary condition on non-convex domains. ：: Mathematische Annalen. 2019 ; 巻 373, 番号 3-4. pp. 1485-1528.
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