Mathematical analysis for interface dynamics of crystal

晶体界面动力学的数学分析

• 批准号: 21740068
• 负责人: ISHIWATA Tetsuya
• 金额: $ 2.83万
• 依托单位: Shibaura Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21740068/
• 关键词: 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; 結晶成長; 形状単調化; 非平面進行波; 応用数学

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.

在这项研究中，我们考虑了一些晶体运动：一种晶体的界面运动。特别地，我们主要讨论了两种类型的晶体运动：具有体效应的晶体曲率流和保持面积的晶体曲率流。讨论了解曲线的行为，而不是渐近行为，对界面线段的消光模式进行了完全的分类，得到了在界面不自相交的条件下解曲线的变形过程.

项目成果

Motion of polygonal curved fronts by crystalline motion: V-shaped solutions and eventual monotonicity,

晶体运动引起的多边形弯曲前沿的运动：V 形解和最终的单调性，

• 发表时间: 2011
• 期刊: Discrete and Continuous Dynamical Systems, Suplement
• 作者: M. Enomoto;T. Ishiwata
• 通讯作者: T. Ishiwata

クリスタライン曲率流による開曲線の運動

由于晶体曲率流动而产生开曲线运动

• 发表时间: 2012
• 作者: K.Anada;T.Ishiwata;T.Ishiwata;T.Ishiwata;T.Ishiwata;石渡哲哉;石渡哲哉
• 通讯作者: 石渡哲哉

Crystalline motion and eventual monotonicity of the shape, The 7th International Congress on Industrial and Applied Mathematics

晶体运动和形状的最终单调性，第七届国际工业与应用数学大会

• 发表时间: 2011
• 作者: K.Anada;T.Ishiwata;T.Ishiwata;T.Ishiwata;T.Ishiwata;石渡哲哉;石渡哲哉;T.Ishiwata;T.Ishiwata;T. Ishiwata;T. Ishiwata
• 通讯作者: T. Ishiwata

Asymptotic behavior of blow-up solutions to a degenerate parabolic equation

简并抛物方程爆炸解的渐近行为

• 发表时间: 2011
• 期刊: Journal of Math-for-Industry
• 作者: T. Ishiwata;K. Anada and T. Ishiwata
• 通讯作者: K. Anada and T. Ishiwata

Motion of infinite length polygonal curves by crystalline curvature flow with a driving force

具有驱动力的晶体曲率流无限长多边形曲线的运动

• 发表时间: 2011
• 作者: K.Anada;T.Ishiwata;T.Ishiwata;T.Ishiwata;T.Ishiwata;石渡哲哉;石渡哲哉;T.Ishiwata;T.Ishiwata;T. Ishiwata;T. Ishiwata;T.Ishiwata;T.Ishiwata;石渡哲哉
• 通讯作者: 石渡哲哉