1997 Fiscal Year Final Research Report Summary
Geometry and Analysis of non-linear Partial Differentail Equations
| 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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| Keywords | Hamilton-Jacobi equations / Conservation laws / Viscosity sokutions / Shock waves / Fascet surfaces / Ginzburg-Landau equations / Lagrangian stability / Cohomology |
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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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Research Products
(37 results)
