Analysis on anisotropic curvature flow equations in phenomena
| Project/Area Number |
18540205
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | The University of Tokyo |
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Principal Investigator |
GIGA Mi-Ho The University of Tokyo, 大学院・数理科学研究科, 特任研究員 (20422397)
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| Co-Investigator(Kenkyū-buntansha) |
ISHII Katsuyuki 神戸大学, 大学院・海事科学研究科, 准教授 (40232227)
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| Project Period (FY) |
2006 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥4,060,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥660,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2007: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2006: ¥1,200,000 (Direct Cost: ¥1,200,000)
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| Keywords | 非線形現象 / 界面運動方程式 / 粘性解 / 非線形偏微分方程式 / 結晶成長 / クリスタライン曲率流 / 自己相似解 / 画像処理 / 曲率流方程式 / 退化放物型方程式 |
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| Research Abstract |
To analyze crystal growth phenomena and image processing technology, various differential equations governing motion of curves or surfaces under a particular law are proposed. We focused on anisotropic curvature flow equations with very singular interfacial energy. We analyzed one of typical equations, so-called a crystalline curvature flow equation. For any initial polygon, we proved the well-posedness of the initial value problem of the corresponding system of ordinary differential equations by using self-similar solutions and a geometric method. On the other hand, we showed that the idea of singular interfacial energy is effective to mathematical analysis of shock waves. Meanwhile anisotropic curvature flow equations with inhomogeneous external force are important to understand crystal growth phenomena. We derived fundamental comparison principle of them.
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Report
(6 results)
Research Products
(25 results)
