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解析学火曜セミナー
過去の記録 ～04/18｜次回の予定｜今後の予定 04/19～
| 開催情報 | 火曜日 16:00～17:30 数理科学研究科棟(駒場) 156号室 |
|---|---|
| 担当者 | 石毛 和弘, 坂井 秀隆, 伊藤 健一 |
| セミナーURL | https://www.ms.u-tokyo.ac.jp/seminar/analysis/ |
2015年05月12日(火)
16:30-18:00 数理科学研究科棟(駒場) 126号室
高棹 圭介 氏 (東京大学大学院数理科学研究科)
Brakkeの平均曲率流に対する制約条件付きAllen-Cahn方程式の収束について (Japanese)
高棹 圭介 氏 (東京大学大学院数理科学研究科)
Brakkeの平均曲率流に対する制約条件付きAllen-Cahn方程式の収束について (Japanese)
[ 講演概要 ]
In this talk we consider the Allen-Cahn equation with constraint. In 1994, Chen and Elliott studied the asymptotic behavior of the solution of the Allen-Cahn equation with constraint. They proved that the zero level set of the solution converges to the classical solution of the mean curvature flow under the suitable conditions on initial data. In 1993, Ilmanen proved the existence of the mean curvature flow via the Allen-Cahn equation without constraint in the sense of Brakke. We proved the same conclusion for the Allen-Cahn equation with constraint.
In this talk we consider the Allen-Cahn equation with constraint. In 1994, Chen and Elliott studied the asymptotic behavior of the solution of the Allen-Cahn equation with constraint. They proved that the zero level set of the solution converges to the classical solution of the mean curvature flow under the suitable conditions on initial data. In 1993, Ilmanen proved the existence of the mean curvature flow via the Allen-Cahn equation without constraint in the sense of Brakke. We proved the same conclusion for the Allen-Cahn equation with constraint.
