The dynamics of curves and surfaces governed by gradient of energy functionals

• Project/Area Number: 19740080
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Global analysis
• Research Institution: Iwate University (2008); Tohoku University (2007)
• Principal Investigator: OKABE Shinya Iwate University, 人文社会科学部, 准教授 (70435973)
• Project Period (FY): 2007 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥2,500,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥300,000); Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2007: ¥1,200,000 (Direct Cost: ¥1,200,000)
• Keywords: 変分法

Research Abstract

当該研究期間において、適当なエネルギー汎函数の勾配に支配される曲線および曲面のダイナミクスについて研究を行った。その結果、次のような成果を得た:(1)一様に強い圧力を受ける弾性閉曲線のダイナミクスについて、圧力が非常に大きい場合に、各平衡点の安定性および不安定性を明らかにすることで、その近傍でのダイナミクスを解明した; (2)閉曲線上で定義されるあるaction 汎函数に対する変分問題に対して、ある動径対称な臨界点の近傍に非動径対称な臨界点が一意に存在することを証明した。

Research Products

• [Journal Article] The dynamics of elastic closed curves under uniform high pressure (2008)
  • Author(s): 岡部真也
  • Journal Title: Calculus of Variations and Partial Differential Equations 33 Pages: 493-521
  • Peer Reviewed
• [Journal Article] The dynamics of an elastic closed curve under uniform high pressure (2008)
  • Author(s): 岡部真也
  • Journal Title: Calculus of Variations and Partial Differential Equations 33, No4 Pages: 493-521
  • Peer Reviewed
• [Journal Article] The motion of elastic planar closed curves under the area preserving condition (2007)
  • Author(s): 岡部真也
  • Journal Title: Indiana Univ. Math. J. 56, No 4 Pages: 1871-1912
  • NAID: 120006459516
  • Peer Reviewed
• [Journal Article] Asymptotic form of solutions of the Tadjbakhsh-Odeh variational problem (2007)
  • Author(s): 岡部真也
  • Journal Title: Advanced Studies in Pure Mathematics 47, No 2 Pages: 709-728
  • Peer Reviewed
• [Journal Article] The motion of elastic planar closed curves under the area-preserving condition (2007)
  • Author(s): 岡部真也
  • Journal Title: Indiana University Mathematics Journal 56-4 Pages: 1871-1912
  • NAID: 120006459516
  • Peer Reviewed
• [Journal Article] Asymptotic form of solutions of the Tadjbakhsh-Odeh variational problem (2007)
  • Author(s): 岡部真也
  • Journal Title: Advanced Studies in Pure Mathematics 47 Pages: 709-728
  • Peer Reviewed
• [Presentation] The variational problem for a certain action functional defined on closed curves (2009)
  • Author(s): 岡部真也
  • Organizer: Mathematical Science and Nonlinear Partial Differential Equations
  • Place of Presentation: 大阪・大阪大学
  • Year and Date: 2009-02-14
• [Presentation] The variational problem for a certain action functional defined on closed curves (2009)
  • Author(s): 岡部真也
  • Organizer: Mathematical Science and Nonlinear Partial Differential Eauations
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-02-14
• [Presentation] The variational problem for a certain action functional defined on closed curves (2009)
  • Author(s): 岡部真也
  • Organizer: 福島応用数学小研究集会
  • Place of Presentation: 福島・福島大学サテライト教室
  • Year and Date: 2009-02-07
• [Presentation] The variational problem for a certain action functional defined on elnsPri eiirvr.R (2009)
  • Author(s): 岡部真也
  • Organizer: 福島応用数学小研究集会
  • Place of Presentation: 福島大学サテライト教室
  • Year and Date: 2009-02-07
• [Presentation] The variational problem for a certain action functional defined on closed curves (2008)
  • Author(s): 岡部真也
  • Organizer: 曲線と曲面の非線形解析
  • Place of Presentation: 大宮・大宮ソニックシティカレッジ
  • Year and Date: 2008-12-18
• [Presentation] The variational problem for a certain action functional defined on closed curves (2008)
  • Author(s): 岡部真也
  • Organizer: 曲線と曲面の非線形解析
  • Place of Presentation: 埼玉大学大宮ソニックシティカレッジ
  • Year and Date: 2008-12-18
• [Presentation] 閉曲線上で定義されたあるaction 汎函数に対する変分問題 (2008)
  • Author(s): 岡部真也
  • Organizer: 2008 年度日本数学会秋季総合分科会
  • Place of Presentation: 東京・東京工業大学
  • Year and Date: 2008-09-25
• [Presentation] 閉曲線上で定義されたあるaction汎函数に対する変分問題 (2008)
  • Author(s): 岡部真也
  • Organizer: 2008年度日本数学会秋季総合分科会
  • Place of Presentation: 東京工業大学
  • Year and Date: 2008-09-25
• [Presentation] The variational problem for a certain action functional defined on closed curves (2008)
  • Author(s): 岡部真也
  • Organizer: 第4回非線型の諸問題
  • Place of Presentation: 佐賀・佐賀大学
  • Year and Date: 2008-09-22
• [Presentation] The variational problem for a certain action functional defined on closed curves (2008)
  • Author(s): 岡部真也
  • Organizer: 第4回非線型の諸問題
  • Place of Presentation: 佐賀大学
  • Year and Date: 2008-09-22
• [Presentation] The variational problem for a certain action functional defined on closed curves (2008)
  • Author(s): 岡部真也
  • Organizer: The 33^<rd> Sapporo Symposium on Partial Differential Equations
  • Place of Presentation: 札幌・北海道大学
  • Year and Date: 2008-08-27
• [Presentation] The variational problem for a certain action functional defined on closed curves (2008)
  • Author(s): 岡部真也
  • Organizer: The 33^<rd> Sapporo Symposium on Partial Differential Equations
  • Place of Presentation: 北海道大学
  • Year and Date: 2008-08-27
• [Presentation] The variational problem for a certain action functional defined on closed curves (2008)
  • Author(s): 岡部真也
  • Organizer: 室蘭工業大学談話会
  • Place of Presentation: 室蘭・室蘭工業大学
  • Year and Date: 2008-07-14
• [Presentation] The variational problem for a certain action functional defined on closed curves (2008)
  • Author(s): 岡部真也
  • Organizer: 室蘭工業大学談話会
  • Place of Presentation: 室蘭工業大学
  • Year and Date: 2008-07-14
• [Presentation] The variational problem for a certain action functional defined on closed curves (2008)
  • Author(s): 岡部真也
  • Organizer: 熊本大学応用解析セミナー
  • Place of Presentation: 熊本・熊本大学
  • Year and Date: 2008-05-10
• [Presentation] The variational problem for a certain action functional defined on closed curves (2008)
  • Author(s): 岡部真也
  • Organizer: 熊本大学応用解析セミナー
  • Place of Presentation: 熊本大学
  • Year and Date: 2008-05-10
• [Presentation] The dynamical aspects of elastic planar closed curves, under uniform High pressure (2008)
  • Author(s): 岡部真也
  • Organizer: 第70回神楽坂解析セミナー
  • Place of Presentation: 東京理科大学
  • Year and Date: 2008-04-28
• [Presentation] The dynamical aspects of elastic closed curves under uniform high pressure (2008)
  • Author(s): 岡部真也
  • Organizer: 第70回神楽坂解析セミナー
  • Place of Presentation: 東京・東京理科大学
  • Year and Date: 2008-04-26
• [Presentation] The dynamics of elastic closed curves under uniform high pressure (2008)
  • Author(s): 岡部真也
  • Organizer: 第7回偏微分方程式ワークショップ
  • Place of Presentation: 鹿児島
  • Year and Date: 2008-03-14
• [Presentation] The dynamics of elastic closed curves under uniform high pressure (2008)
  • Author(s): 岡部真也
  • Organizer: 第7回偏微分方程式ワークショップ
  • Place of Presentation: マリンパレスかごしま
  • Year and Date: 2008-03-14
• [Presentation] The dynamical aspects of elastic closed curves under uniform high pressure (2008)
  • Author(s): 岡部真也
  • Organizer: The 9^<th> Northeastern Symposium on Mathematical Analysis
  • Place of Presentation: 札幌・北海道大学
  • Year and Date: 2008-02-21
• [Presentation] The dynamical aspects of elastic closed curves under uniform high pressure (2008)
  • Author(s): 岡部真也
  • Organizer: The 9th Northeastern Symposium on Mathematical Analysis
  • Place of Presentation: 北海道大学
  • Year and Date: 2008-02-21
• [Presentation] The dynamics of elastic closed curves under uniform high pressure (2008)
  • Author(s): 岡部真也
  • Organizer: 変分問題セミナー
  • Place of Presentation: 東京・首都大学東京
  • Year and Date: 2008-01-18
• [Presentation] The dynamics of elastic closed curves under uniform high pressure (2008)
  • Author(s): 岡部真也
  • Organizer: 首都大学東京変分問題セミナー
  • Place of Presentation: 首都大学東京
  • Year and Date: 2008-01-18
• [Presentation] The stability and instability of elastic closed curves under uniform high pressure (2007)
  • Author(s): 岡部真也
  • Organizer: 第5回浜松偏微分方程式研究集会
  • Place of Presentation: 浜松・静岡大学
  • Year and Date: 2007-12-18
• [Presentation] The stability and instability of elastic closed curves under uniform high pressure (2007)
  • Author(s): 岡部真也
  • Organizer: 第5回浜松偏微分方程式研究集会
  • Place of Presentation: 静岡大学
  • Year and Date: 2007-12-18
• [Presentation] The structure of solutions of Tadjbakhsh-Odeh variational problem with large pressure term (2007)
  • Author(s): 岡部真也
  • Organizer: Asia PDE mini-warkshop at Sendai
  • Place of Presentation: 仙台・東北大学
  • Year and Date: 2007-09-13
• [Presentation] The structure of solutions Tadjbakhsh-Odeh variational problem with large pressure term (2007)
  • Author(s): 岡部真也
  • Organizer: Asia PDE mini-workshop at Sendai
  • Place of Presentation: 東北大学
  • Year and Date: 2007-09-13
• [Presentation] あるエネルギー汎函数の勾配に支配される曲線のダイナミクス (2007)
  • Author(s): 岡部真也
  • Organizer: 東北大学数学教室談話会
  • Place of Presentation: 仙台・東北大学
  • Year and Date: 2007-06-04
• [Presentation] あるエネルギー汎函数の勾配に支配される曲線のダイナミクス (2007)
  • Author(s): 岡部真也
  • Organizer: 東北大学数学教室談話会
  • Place of Presentation: 東北大学
  • Year and Date: 2007-06-04
• [Presentation] The dynamics of elastic closed curves under uniform high pressure (2007)
  • Author(s): 岡部真也
  • Organizer: 九州函数方程式セミナー
  • Place of Presentation: 福岡・九州大学
  • Year and Date: 2007-05-25
• [Presentation] The dynamics of elastic closed curves under uniform high pressure (2007)
  • Author(s): 岡部真也
  • Organizer: 九州関数方程式セミナー
  • Place of Presentation: 九州大学
  • Year and Date: 2007-05-25
• [Presentation] 一様に強い圧力を受ける平面弾性閉曲線のダイナミクス (2007)
  • Author(s): 岡部真也
  • Organizer: 月曜解析セミナー
  • Place of Presentation: 仙台・東北大学
  • Year and Date: 2007-05-21
• [Presentation] -様に強い圧力をうける平面弾性閉曲線のダイナミクス (2007)
  • Author(s): 岡部真也
  • Organizer: 月曜解析セミナー
  • Place of Presentation: 東北大学
  • Year and Date: 2007-05-21