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解析学火曜セミナー
過去の記録 ～04/19｜次回の予定｜今後の予定 04/20～
| 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/ |
2022年05月31日(火)
16:00-17:30 数理科学研究科棟(駒場) 126号室
対面・オンラインハイブリッド開催（対面は本学関係者のみに限定します）
岡部真也 氏 (東北大学)
Convergence of Sobolev gradient trajectories to elastica (Japanese)
https://forms.gle/wkCbqdmNuz9zr3vA8
対面・オンラインハイブリッド開催（対面は本学関係者のみに限定します）
岡部真也 氏 (東北大学)
Convergence of Sobolev gradient trajectories to elastica (Japanese)
[ 講演概要 ]
In this talk we consider a higher order Sobolev gradient flow for the modified elastic energy defined on closed space curves. The $L^2$-gradient flow for the modified elastic energy has been well studied, and standard results are solvability of the flow for smooth initial curve and subconvergence of solutions to elastica. Moreover, stronger convergence results, so called full limit convergence, are generally up to reparametrisation and sometimes translation. In this talk, we consider $H^2$-gradient flow for the modified elastic energy and prove (i) the solvability of the flow for initial curve in the energy class, (ii) full limit convergence to elastica by way of a Lojasiewicz—Simon gradient inequality. This talk is based on a joint work with Philip Schrader (Murdoch University).
[ 参考URL ]In this talk we consider a higher order Sobolev gradient flow for the modified elastic energy defined on closed space curves. The $L^2$-gradient flow for the modified elastic energy has been well studied, and standard results are solvability of the flow for smooth initial curve and subconvergence of solutions to elastica. Moreover, stronger convergence results, so called full limit convergence, are generally up to reparametrisation and sometimes translation. In this talk, we consider $H^2$-gradient flow for the modified elastic energy and prove (i) the solvability of the flow for initial curve in the energy class, (ii) full limit convergence to elastica by way of a Lojasiewicz—Simon gradient inequality. This talk is based on a joint work with Philip Schrader (Murdoch University).
https://forms.gle/wkCbqdmNuz9zr3vA8
