| Project/Area Number |
22740110
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Global analysis
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| Research Institution | Kanagawa University |
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Principal Investigator |
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 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 |
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| Research Abstract |
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.
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