| Project/Area Number |
25400156
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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 | Saitama University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
TACHIKAWA Atsusi 東京理科大学, 理工学部, 教授 (50188257)
YAZAKI Shigetoshi 明治大学, 理工学部, 教授 (00323874)
KOHSAKA Yoshihito 神戸大学, 大学院海事科学研究科, 准教授 (00360967)
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 一般化された回転超曲面 / メビウス・エネルギー / メビウス不変性 / 変分公式 / 変分問題 / 分解されたメビウス・エネルギー / 離散エネルギー / 一般化された超曲面 / 分解定理 |
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| Outline of Final Research Achievements |
When we deal with variational problems for hypersurfaces, some difficulties may occur. Assuming some symmetry, the problems can be reduced to the problem of curves. Here we obtain three kind of results. First, we reduce the inelastic collision of elastic shell to the problem of centerline, and propose a mathematical model and perform numerical simulation. Secondly, we study the global existence of rotational hypersurface with prescribed mean curvature. The problem can be reduced to the global existence of solutions of an ordinary differential equation which the generating curve satisfies. We resolve the problem completely for all types of hypersurfaces. Lastly we deal with the Moebius energy. We show that the energy can be decomposed into three parts keeping the Moebius invariance. By ude of the decomposition. the variational formulas are derived explicitly. Furthermore we have their estimates on several function spaces.
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