Inverse problems and nonlinear integral transforms
| Project/Area Number |
21540165
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Tokyo University of Marine Science and Technology |
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Principal Investigator |
KAMIMURA Yutaka 東京海洋大学, 海洋科学技術研究科, 教授 (50134854)
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| Project Period (FY) |
2009 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 関数方程式 / 逆問題 / 非線形大域理論 / 周期運動 / 復元力 / 移流拡散 / 微分方程式 / 非線形積分変換 / 逆分岐問題 / 大域分岐 / 非線形項 / 振幅 / 周期 / 半周期 / 常微分方程式 / 第一分岐 / 大域存在定理 |
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| Research Abstract |
We establish a theory of a nonlinear integral transform and obtain a global theorem for an inverse problem in bifurcation theory. Based upon the result we consider a problem of determining a nonlinearity of an autonomous differential equation of a period function, namely, a relation between periods and amplitudes to prove a global existence of nonlinear terms realizing a prescribed, Lipschitz continuous period function and characterize the nonlinear terms. This gives a complete answer to a classical inverse problem in a nonlinear autonomous oscillation.
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Report
(5 results)
Research Products
(33 results)
