| Project/Area Number |
25610025
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical analysis
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| Research Institution | The University of Tokyo |
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Principal Investigator |
GIGA Yoshikazu 東京大学, 大学院数理科学研究科, 教授 (70144110)
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| Research Collaborator |
ASAI Tomoro
OHTSUKA Takeshi
GIGA Mi-Ho
KURODA Hirotoshi
NAKAYASU Atsushi
HAMAMUKI Nao
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 粘性解 / 距離空間 / ハミルトン・ヤコビ方程式 / アイコナール方程式 / クリスタライン曲率 / 表面拡散流方程式 / 平均曲率流方程式 / 距離 / 自己相似解 / 一意存在 / 安定性 / 比較定理 / 劣最適性 / 勾配流 |
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| Outline of Final Research Achievements |
We consider the Eikonal equation in a space such as network or fractal, where the gradient of function is not well-defined in canonical way. We establish the theory of viscosity solutions in a general metric space. We also establish the theory of viscosity solutions for a curvature flow equation describing motion of a surface of a crystal or a grain boundary, especially a crystalline curvature flow, which has a strong anisotropy, when the surface is regarded as a curve. A curvature flow with strong anisotropy is regarded at least formally as a gradient flow of area measured by non-Euclidean metric in a suitable metric space. However, a general theory is not yet established so we study the problem individually.
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