Free boundary problems described by vectorial order parameters

由向量阶参数描述的自由边界问题

• 批准号: 21740120
• 负责人: SHIRAKAWA Ken
• 金额: $ 2.66万
• 依托单位: Chiba University (2010-2011)Kobe University (2009)
• 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-21740120/
• 关键词: 非線形現象; 自由境界問題; ベクトル値の相関数; 変分学; 安定性; 幾何学的構造固体・液体相転移; 薄膜磁性体; 幾何学的構造; 退化型の材料係数; 固体・液体相転移; Allen-Cahn型方程式; 最適制御問題; 数値実験; 多角形構造; 自由境界の幾何学的形状; 退化性を伴うエネルギー; Г-収束; 状態分布関数; ベクトル値の設定; スカラー値の設定; 自由境界; 全変動汎関数; 変分構造

The objective in this study is to understand the deformation process of free boundaries from variational and geometric viewpoint. To this end, some free boundary problems appearing in two phenomena : solid-liquid phase transition ; ferromagnetic thin film ; were dealt with. On that basis, various study results were reported during the research period. Especially, it will be notable that some obtained results are concerned with more advanced themes than originally expected : optimal control problem ; numerical experiments for optimal controls.

本研究的目的是从变分和几何的角度理解自由边界的变形过程。为此，一些自由边界问题出现了两种现象：固液相变；铁磁薄膜；被处理了。在此基础上，研究期间报告了各种研究结果。特别是，值得注意的是，一些获得的结果涉及比最初预期更高级的主题：最优控制问题；最佳控制的数值实验。