On a dynamics of a solution for geometric evolution equations with a variational structure

• Project/Area Number: 20740086
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Global analysis
• Research Institution: Muroran Institute of Technology
• Principal Investigator: KOHSAKA Yoshihito 室蘭工業大学, 大学院・工学研究科, 准教授 (00360967)
• Project Period (FY): 2008 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 表面拡散方程式 / 平均曲率一定曲面 / Willmore流方程式 / 平均曲率流方程式 / 曲率流方程式 / 3相境界 / 分岐解析 / 境界付き曲面 / 曲線短縮方程式 / 特異点 / 境界付き超曲面 / 平均曲率流

Research Abstract

The motion of three hypersurfaces by mean curvature flow is studied. These hypersurfaces intersect each other. The existence of a local-in-time solution to an initial and boundary value problem for a system of nonlinear parabolic partial differential equations with non-local term is showed. Also, the motion of an axisymmetric surface by surface diffusion equation is studied. In order to obtain the linearized stability of a stationary surface, a corresponding eigenvalue problem is derived and analyzed.

Research Products

• [Journal Article] On evolving hypersurfaces with boundaries by mean curvature flow (2011)
  • Author(s): D.Depner, H.Garcke, Y.Kohsaka
  • Journal Title: 数理解析研究所講究録 Volume: 1740 Pages: 24-36
• [Journal Article] Surface diffusion with triple junctions : A stability criterion for stationarySolutions (2010)
  • Author(s): H. Garcke、K. Ito、Y. Kohsaka
  • Journal Title: Advances in DifferentialEquations Volume: vol. 15 Pages: 437-472
  • Peer Reviewed
• [Journal Article] Surface diffusion with triple junctions : A stability criterion for stationary solutions (2010)
  • Author(s): H.Garcke, K.Ito, Y.Kohsaka
  • Journal Title: Advances in Differential Equations 15 Pages: 437-472
• [Journal Article] Surface diffusion with triple junctions : A stability criterion for stationary solutions (2010)
  • Author(s): H.Garcke, K.Ito, Y.Kohsaka
  • Journal Title: Advances in Differential Equations Volume: 15 Pages: 437-472
  • Peer Reviewed
• [Journal Article] Stability analysis of phase boundarymotion by surface diffusion with triplejunction (2009)
  • Author(s): H. Garcke、K. Ito、Y. Kohsaka
  • Journal Title: Banach Center Publications Volume: vol. 87 Pages: 83-101
  • Peer Reviewed
• [Journal Article] Nonlinear stability of stationarysolutions for curvature flow withtriple junction (2009)
  • Author(s): H. Garcke、Y. Kohsaka、D. Sevcovic
  • Journal Title: Hokkaido Mathematical Journal Volume: vol. 38 Pages: 721-769
  • Peer Reviewed
• [Journal Article] Stability analysis of phase boundary motion by surface diffusion with triple junction (2009)
  • Author(s): H.Garcke, K.Ito, Y.Kohsaka
  • Journal Title: Banach Center Publications 87 Pages: 83-101
  • Peer Reviewed
• [Journal Article] Nonlinear stability of stationary solutions for curvature flow with triple junction (2009)
  • Author(s): H.Garcke, Y.Kohsaka, D.Sevcovic
  • Journal Title: Hokkaido Mathematical Journal 38 Pages: 721-769
  • Peer Reviewed
• [Presentation] Motion of interfaces bysurface diffusion equation (2012)
  • Author(s): 高坂良史
  • Organizer: 研究集会「非線形現象の数値シミュレーションと解析2012」
  • Place of Presentation: 北海道大学
  • Year and Date: 2012-03-09
• [Presentation] Motion of interfaces by surface diffusion equation (2012)
  • Author(s): 高坂良史
  • Organizer: 非線形現象の数値シミュレーションと解析2012
  • Place of Presentation: 北海道大学(招待講演)
  • Year and Date: 2012-03-09
• [Presentation] Stability and instability ofstationary interfaces for surfacediffusion equation (2011)
  • Author(s): 高坂良史
  • Organizer: 弘前非線形方程式研究会
  • Place of Presentation: 弘前大学
  • Year and Date: 2011-12-22
• [Presentation] Stability and instability of stationary interfaces for surface diffusion equation (2011)
  • Author(s): 高坂良史
  • Organizer: 弘前非線形方程式研究会
  • Place of Presentation: 弘前大学(招待講演)
  • Year and Date: 2011-12-22
• [Presentation] Stability analysis of steadystates for surface diffusion equation ina bounded domain (2010)
  • Author(s): 高坂良史
  • Organizer: 学際的国際会議とチュートリアルセミナー「結晶成長の数学的側面」
  • Place of Presentation: 北海道大学
  • Year and Date: 2010-07-30
• [Presentation] Stability analysis of steady states for surface diffusion equation in a bounded domain (2010)
  • Author(s): 高坂良史
  • Organizer: 学際的国際会議とチュートリアルセミナー「結晶成長の数学的側面」
  • Place of Presentation: 北海道大学
  • Year and Date: 2010-07-30
• [Presentation] On evolving hypersurfaceswith boundaries by mean curvature flow (2010)
  • Author(s): 高坂良史
  • Organizer: 研究集会「変分問題の展開-幾何学的勾配流と臨界点理論の新潮流」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2010-06-07
• [Presentation] On evolving hypersurfaces with boundaries by mean curvature flow (2010)
  • Author(s): 高坂良史
  • Organizer: 研究集会「変分問題の展開-幾何学的勾配流と臨界点理論の新潮流」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2010-06-07
• [Presentation] Motion of phase boundaries bygeometric evolution equations (2010)
  • Author(s): 高坂良史
  • Organizer: Oberwolfach Workshop
  • Place of Presentation: Oberwolfach(ドイツ)
  • Year and Date: 2010-02-02
• [Presentation] Motion of phase boundaries by geometric evolution equations (2010)
  • Author(s): 高坂良史
  • Organizer: Oberwolfach Workshop
  • Place of Presentation: Oberwolfach(ドイツ)
  • Year and Date: 2010-02-02
• [Presentation] Motion of phase boundaries by geometric evolution equations (2010)
  • Author(s): 高坂良史
  • Organizer: Oberwolfach Workshop
  • Place of Presentation: Oberwolfach
  • Year and Date: 2010-02-02
• [Presentation] Phase boundary motionby surface diffusion with triple junction (2008)
  • Author(s): 高坂良史
  • Organizer: SIAM Conference on MathematicalAspects of Materials Science
  • Place of Presentation: Philadelphia(アメリカ)
  • Year and Date: 2008-05-13
• [Presentation] Phase boundary motion by surface diffusion with triple junction (2008)
  • Author(s): 高坂良史
  • Organizer: SIAM Conference on Mathematical Aspects of Materials Science
  • Place of Presentation: Philadelphia (アメリカ)
  • Year and Date: 2008-05-13
• [Presentation] Phase boundary motion by surface diffusion with triple junction (2008)
  • Author(s): 高坂良史
  • Organizer: SIAM Conference on Mathematical Aspects of Materials Science
  • Place of Presentation: Philadelphia
  • Year and Date: 2008-05-13
• [Remarks]
  • URL: http://www.mmm.muroran-it.ac.jp/~kohsaka/main.html