| Project/Area Number |
08454011
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | HOKKAIDO UNIVERSITY |
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Principal Investigator |
IZUMIYA Shyuichi Hokkaido University, Graduate school of science, Professor, 大学院・理学研究科, 教授 (80127422)
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| Co-Investigator(Kenkyū-buntansha) |
ISHIKAWA Goo Hokkaido University, Graduate school of science, Associate professor, 大学院・理学研究科, 助教授 (50176161)
KIYOHARA Kazuyosi Hokkaido University, Graduate school of science, Associate professor, 大学院・理学研究科, 助教授 (80153245)
OZAWA Toru Hokkaido University, Graduate school of science, Professor, 大学院・理学研究科, 教授 (70204196)
GIGA Yosikazu Hokkaido University, Graduate school of science, Professor, 大学院・理学研究科, 教授 (70144110)
YAMAGUCHI Keizou Hokkaido University, Graduate school of science, Professor, 大学院・理学研究科, 教授 (00113639)
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| Project Period (FY) |
1996 – 1997
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| Project Status |
Completed (Fiscal Year 1997)
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| Budget Amount *help |
¥8,500,000 (Direct Cost: ¥8,500,000)
Fiscal Year 1997: ¥4,100,000 (Direct Cost: ¥4,100,000)
Fiscal Year 1996: ¥4,400,000 (Direct Cost: ¥4,400,000)
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| Keywords | Hamilton-Jacobi equations / Conservation laws / Viscosity sokutions / Shock waves / Fascet surfaces / Ginzburg-Landau equations / Lagrangian stability / Cohomology / ギンツブルクランダウ方程式 / シンプレクティック多様体 / 非線形偏微分方程式 / ハミルトン・ヤコビ方程式 / ルジャンドル組み紐 / シュレディンガー方程式 |
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| Research Abstract |
In this research project, we established the calssification of the singularities of solution surfaces of quasi-homogeneous first order partial differential equations, viscosity solutions of Hamilton-Jacobi equations with one-space variable and multivalued solutions of conservation laws which are a part of the main purpose. Moreover, we extend the theory ofviscosity solutions to the case when the second order non-degenerate equation with non-local effects (one-space variable). This research is important to describe the crystal growth with fascet surfaces. We also give some iimportant new examples of Riemannian manifolds with integrable geodesic flows.
On the other hand, we have shown the existence of stable solutions for Ginzburg-Landau equation in a rotain domain. We have given a characterization of the symplectic and Lagarangian stablity of isotropic submanifolds with corank one by using a kind of transversality theorem. As a result on Algebraic and Geometric Topology we have developed an elementary tools for calculating the cohomology of heyper eliptic mapping class groups over finite fields.
These results are contained in the areas of the border of Geometry and Analysis. We expect to apply these results for studying Partial Differentail Equations in near future.
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