Mathematical analysis for interface dynamics of crystal

2011 Fiscal Year Final Research Report

• Project/Area Number: 21740068
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Shibaura Institute of Technology
• Principal Investigator: ISHIWATA Tetsuya 芝浦工業大学, システム理工学部, 准教授 (50334917)
• Project Period (FY): 2009 – 2011
• Keywords: 界面ダイナミクス / 結晶界面 / 曲率流 / 解の挙動 / 進行波 / 非線形現象 / 数理モデル

Research Abstract

In this research, we consider some crystalline motions : a kind of interface motion of crystal. In particular, we mainly treat 2 types of crystalline motion : crystalline curvature flow with bulk effect and area-preserving crystalline curvature flow. We discuss the behavior of solution curves, not asymptotic behavior, and classify the extinction patterns of a line-segment of the interface completely and obtain the deformation process of solution curve under the conditions for no self-intersection of the interface.

Research Products

• [Journal Article] Motion of essentially admissible V-shaped polygonal curves governed by generalized crystalline motion with a driving force (2011)
  • Author(s): T. Ishiwata
  • Journal Title: Journal of Math-for-Industry Volume: Vol.3 Pages: 21-25
  • URL: http://gcoe-mi.jp/english/temp/publish/098d0a97160e4eacbdcfe54542c293c3.pdf
• [Journal Article] Asymptotic behavior of blow-up solutions to a degenerate parabolic equation (2011)
  • Author(s): K. Anada and T. Ishiwata
  • Journal Title: Journal of Math-for-Industry Volume: Vol.3 Pages: 1-8
  • URL: http://gcoe-mi.jp/english/temp/publish/b381507677a68af7d14357dba61a72a4.pdf
• [Journal Article] Motion of polygonal curved fronts by crystalline motion : V-shaped solutions and eventual monotonicity (2011)
  • Author(s): T. Ishiwata
  • Journal Title: Discrete and Continuous Dynamical Systems, Supplement Volume: Volume 1 Pages: 717-726
• [Journal Article] On the motion of polygonal curves with asymptotic lines by crystalline curvature flow with bulk effect (2011)
  • Author(s): T. Ishiwata
  • Journal Title: Discrete and Continuous Dynamical Systems Series S Volume: vol.4, no.4 Pages: 865-873
  • URL: http://aimsciences.org/journals/displayArticles.jsp?paperID=5705
• [Presentation] Behavior of polygonal curves by crystalline curvature flow, Dutch-Japanese Workshop, Analysis of non-equilibrium evolution problems : selected topics in material and life sciences (2011)
  • Author(s): T. Ishiwata
  • Organizer: Eindhoven University of Technology
  • Place of Presentation: Netherlands
  • Year and Date: 20110800
• [Presentation] Behavior of Polygonal Curves by Crystalline Curvature Flow, Workshop on Nonlinear Partial Differential Equations (2011)
  • Author(s): T. Ishiwata
  • Organizer: Dept of Math and Center of PDE
  • Place of Presentation: East China Normal University,上海
  • Year and Date: 20110300
• [Presentation] Motion of non-closed planar polygonal curves by crystalline curvature flow with a driving force (2011)
  • Author(s): T. Ishiwata
  • Organizer: From-Equilibrium Dynamics 2011
  • Place of Presentation: Kyoto, Japan
  • Year and Date: 20110104-08
• [Presentation] Behavior of polygonal curves by crystalline curvature flow with a driving force (2011)
  • Author(s): T. Ishiwata
  • Organizer: East Asia section of SIAM 2011
  • Place of Presentation: Waseda Univ. Kita-Kyushu campus
  • Year and Date: 2011-07-29
• [Presentation] Crystalline motion and eventual monotonicity of the shape, The 7th International Congress on Industrial and Applied Mathematics (2011)
  • Author(s): T. Ishiwata
  • Organizer: Vancouver Convention Centre
  • Place of Presentation: Vancouver, BC, Canada
  • Year and Date: 2011-07-19
• [Presentation] Motion of non-closed planar polygonal curves by crystalline motion (2010)
  • Author(s): 石渡哲哉
  • Organizer: 応用数学合同研究集会
  • Place of Presentation: 龍谷大学瀬田キャンパス
  • Year and Date: 2010-12-17
• [Presentation] Crystalline motion and eventual monotonicity of the shape (2010)
  • Author(s): T. Ishiwata
  • Organizer: Czech-Japanese Semilar in Applied Mathematics
  • Place of Presentation: Czech Technical University, Prague, Czech Republic
  • Year and Date: 2010-08-30
• [Presentation] Motion of polygonal curved fronts by crystalline motion : V-shaped solutions and eventual monotonicity (2010)
  • Author(s): T. Ishiwata
  • Organizer: The 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications
  • Place of Presentation: Dresden University of Technology, Dresden, Germany
  • Year and Date: 2010-05-26
• [Presentation] On the motion of polygonal curves by crystalline curvature flow with bulk effect (2009)
  • Author(s): T. Ishiwata
  • Organizer: 1st Italian-Japanese workshop on geometric properties for parabolic and elliptic PDE's
  • Place of Presentation: Tohoku University, Sendai, Japan
  • Year and Date: 2009-06-16