2017 Fiscal Year Final Research Report
Mathematical analysis and development of free boundary problems arising in grain boundary motion phenomena
| Project/Area Number |
26400179
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Mathematical analysis
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| Research Institution | Kanagawa University |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Keywords | 関数方程式 / 実函数論 / 最適制御 / 自由境界 |
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| Outline of Final Research Achievements |
In this research project, we showed the existence and properties of solutions to the grain boundary motion model of Kobayashi--Warren--Carter type. In addition, we considered the singular limit problem of the Allen--Cahn equation with nonlinear constraint that is the subdifferential of the indication function on the closed interval [-1, 1]. Then, we proved the existence and properties of the singular limit of solutions and the subdifferential of the indication function. Furthermore, we showed the stability conditions for numerical experiments on the Allen-Cahn equation with the Yosida approximation term, and performed numerical experiments of our problems by using the discrete algorithms proposed in this research project.
We also considered optimal control problems of various phase change models, and established the theory of singular optimal control problems to abstract nonlinear evolution equations governed by time-dependent subdifferentials.
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| Free Research Field |
非線形実凸解析学
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