Analysis of mathematical model of grain boundary motions in materials and evolution of mathematical theory

材料晶界运动数学模型分析及数学理论演化

• 批准号: 22740110
• 负责人: YAMAZAKI NORIAKI
• 金额: $ 2.25万
• 依托单位: Kanagawa University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010-04-01 至 2014-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22740110/
• 关键词: 関数方程式; 非線形解析; 非線形現象; 自由境界; 最適制御; 関数方程式論; 実函数論; 力学系; 相転移現象; 特異拡散; 実函教諭

In this research project, we consider mathematical models of grain boundary motions in materials, which is a Kobayashi-Warren-Carter type. Then, we showed the asymptotic behavior of solutions, the existence and stability of stationary solutions and the existence and characterization of attractors. Also, we proved the solvability of the original Kobayashi-Warren-Carter model of grain boundary motions. Moreover, we showed the existence of solutions to a system of Allen-Cahn equation and grain boundary motion model of Kobayashi-Warren-Carter type. Also, we studied optimal control problems for phase field system with total variation functional as the interfacial energy. Then, we proved the existence of an optimal control that minimizes the nonlinear and nonsmooth cost functional. Moreover, we showed the necessary condition of the optimal pair.

在本研究计划中，我们考虑材料中晶界运动的数学模型，这是一个小林-沃伦-卡特类型。然后，我们证明了解的渐近性态、定态解的存在性和稳定性以及吸引子的存在性和特征。此外，我们还证明了原Kobayashi-Warren-Carter晶界运动模型的可解性。此外，我们还证明了Allen-Cahn方程组和Kobayashi-Warren-Carter型晶界运动模型解的存在性。研究了以总变差泛函为界面能的相场系统的最优控制问题。然后，我们证明了最优控制的存在性，使非线性和非光滑的成本功能。此外，我们还证明了最优对的必要条件。

项目成果

Necessary conditions for optimal control of positive solutions to second order impulsive differential equations

二阶脉冲微分方程正解最优控制的必要条件

• 发表时间: 2013
• 作者: 山崎教昭;L. Zhang;C. Zhai
• 通讯作者: C. Zhai

Global solvability of a model for grain boundary motion with constraint

带约束的晶界运动模型的全局可解性

• 发表时间: 2012
• 期刊: Discrete and Continuous Dynamical Systems, Series S
• 作者: 伊藤 昭夫;剣持 信幸;山崎 教昭
• 通讯作者: 山崎 教昭

Global attractor of the multivalued semigroup associated with a phase-field model of grain boundary motion with constraint

与约束晶界运动相场模型相关的多值半群的全局吸引子

• 发表时间: 2011
• 期刊: Dynamical Systems, Differential Equations and Applications, Discrete and Continuous Dynamical Systems
• 作者: T. Ohtsuka; K. Shirakawa and N. Yamazaki;大塚岳;篠原知子;N. Kenmochi and N. Yamazaki
• 通讯作者: N. Kenmochi and N. Yamazaki

Some characterization of attractor for a grain boundary motion model with constraint

带约束的晶界运动模型吸引子的一些表征

• 发表时间: 2011
• 作者: 山崎教昭;剣持信幸
• 通讯作者: 剣持信幸

Large-time behavior of solutions to a phase-field model of grain boundary motion with constraint, Current Advances in Nonlinear Analysis and Related Topics

带约束的晶界运动相场模型解的大时间行为，非线性分析及相关主题的最新进展

• 发表时间: 2010
• 期刊: GAKUTO Internat. Ser. Math. Sci. Appl
• 作者: Rei Inoue;Osamu Iyama;Bernhard Keller;Atsuo Kuniba and Tomoki Nakanishi;N. Kenmochi and N. Yamazaki
• 通讯作者: N. Kenmochi and N. Yamazaki