2013 Fiscal Year Final Research Report
Research on inverse problems and boundary control problems for partial differential equations having transport and nonlocal terms
| Project/Area Number |
23540240
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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 |
Global analysis
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| Research Institution | Kobe University |
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Principal Investigator |
NAKAGIRI Shin-ichi 神戸大学, 大学院システム情報学研究科, 名誉教授 (20031148)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 関数解析 / 逆問題 / 移流拡散方程式 / ボルテラ型微分積分方程式 / 変形公式 / スペクトル解析 / 境界制御 / 最適制御 |
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| Research Abstract |
Inverse problems and boundary control problems for partial differential equations having transport and nonlocal terms are investigated by the method of deformation formulas. For the transport diffusion equations, the investigator has determined uniquely the transport term by boundary observaton, and for the associated control system having nonlocal terms, he has constructed a concrete boundary feedback control law which makes the system a desirable stable state. The key to solve the problems is to use the deformation formula which deforms the transport term and nonlocal terms simultaneously, and the investigator has solved the problem of existence and construction of such a deformation kernel function. In addition, the deformation formula is extended to a system of first order Volterra integro-differential equations. By using the kernel, he has solved the related inverse and boundary control problems for the Volterra system.
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