2016 Fiscal Year Final Research Report
Existence theorems in inverse problems
| Project/Area Number |
26400159
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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 | Tokyo University of Marine Science and Technology |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Keywords | 逆問題 / 微分方程式 / 非線形解析 / エネルギー依存逆散乱 / 逆爆発問題 |
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| Outline of Final Research Achievements |
This research has established the reconstruction formula, the existence theorem, and the identification theorem of an inverse problem of determining velocity field and diffusivity from tracer data. In connection with this inverse problem, the research has deduced a reconstruction formula of potential in an energy dependent inverse scattering, based on which it has established the existence theorem of the potential in the reflectionless scattering with one bound state. In addition, this research has studied an inverse problem to determine a nonlinearity of an differential equation from blow-up time of solutions to the equation to establish a global existence theorem for the inverse problem. A new general method on nonlinear analysis has been found by making mathematical structure of these inverse problems clear.
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| Free Research Field |
数物系科学
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