| Project/Area Number |
16K05218
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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 | Hokkaido University |
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Principal Investigator |
JIMBO Shuichi 北海道大学, 理学研究院, 教授 (80201565)
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| Co-Investigator(Kenkyū-buntansha) |
本多 尚文 北海道大学, 理学研究院, 教授 (00238817)
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| Research Collaborator |
Ito Hiroya
Ushikoshi Erika
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 特異的領域変形 / 楕円型方程式系 / スペクトル解析 / 楕円型作用素 / 弾性体方程式 / 極端領域 / スペクトル / 漸近公式 / 特異的領域 / 固有値問題 / 摂動公式 / 極端形状領域 |
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| Outline of Final Research Achievements |
Eigenfrequencies of an elastic body of uniform and isotropic material but with an extremely thin shape with non-uniform cross-section are studied. The distribution of eigenvalues and their structure was analyzed. The eigenfrequencies of the bending mode were proved to be very small for thinner limit and elaborate behavior were described by the aid of a certain 4-th order ODE operator with variable coefficients. The eigenfrequencies corresponding to the Stretching mode and the Torsion mode are also analyzed and the limiting behavors were described by a certain 2nd order ODE operator, respectively in the case that the thin domain is axissymmetric. The spectum of the elliptic opeator which arises as a vibration model in the geophysics was studied and it is proved that the essential spectrum is bounded in the comples plain while discrete spectrum is unbounded.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究は力学的な自然現象のモデル方程式の数学解析を行っている. 建物や橋の構造などの運動に関連する方程式のスペクトル解析を行った. これらは物体の振動や安定性などの解析に密接に関連する数学理論である. 偏微分方程式理論では単独の楕円型方程式に対してこのような特異的な形状依存性の研究が従来行われてきたが, 本研究では上記のように身近の物理現象に関連する課題に密接に関連する数学的成果を得たことが意義が深いと思われる.
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