| Project/Area Number |
15K17543
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Hiroshima University |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 微分式系 / 外微分式系 / 田中理論 / 微分方程式の幾何学 / フィンスラー幾何学 / 微分幾何学 / 微分形式 |
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| Outline of Final Research Achievements |
A subbundle of the tangent bundle on a manifold is called a differential system.
The theory of differential systems is known as a method to study partial differential equations, geometrically. Moreover, the theory of exterior differential systems which is a generalization of differential systems is also useful for the geometrical study of partial differential equations. On the other hands, partial differential equations are used to describe natural phenomena, therefore to study partial differential equations is important. In this situation, we apply the theory of differential systems and exterior differential systems to partial differential equations, especially, higher order or multi unknown functions partial differential equations. we clarify basic and fundamental properties for the equations.
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| Academic Significance and Societal Importance of the Research Achievements |
微分方程式は自然現象、社会現象を科学的に記述、研究するために極めて重要な研究対象であり、また、個別の微分方程式ではなく、統一的に微分方程式を扱い、その共通の性質を明らかにすることは意義の有ることである。一方で、微分方程式の持つ幾何学的性質を明らかにすること、また逆に幾何学的に重要な性質を持つ対象を微分方程式から構成することは微分幾何学の視点からも意義のあることである。
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