Inverse Problems in Nonlinear Phenomena
| Project/Area Number |
15540201
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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 |
Global analysis
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| Research Institution | Tokyo University of Marine Science and Technology (2004-2006)
東京水産大学 (2003) |
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Principal Investigator |
KAMIMURA Yutaka Tokyo University of Marine Science and Technology, Faculty of Marine Science, Professor, 海洋科学部, 教授 (50134854)
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| Co-Investigator(Kenkyū-buntansha) |
IWASAKI Katsunori Tokyo University of Marine Science and Technology, Faculty of Mathematics, Professor, 大学数理学研究院, 教授 (00176538)
TSUBOI Kenji Tokyo University of Marine Science and Technology, Faculty of Marine Science, Professor, 海洋科学部, 教授 (50180047)
NAKASHIMA Kimie Tokyo University of Marine Science and Technology, Faculty of Marine Science, Associate Professor, 海洋科学部, 助教授 (10318800)
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| Project Period (FY) |
2003 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 2006: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2005: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2004: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2003: ¥800,000 (Direct Cost: ¥800,000)
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| Keywords | energy dependent scattering / inverse scattering problem / inverse problem / Schrodinger equation / Marchenko equation / potentials / 移流拡散方程式 / 再構成法 / マルチェンコ方程式 / シュレディンガー方程式 / クライン・ゴードン方程式 / 非線形問題 / Marchenkoの方程式 / カオス / 周期軌道 / モデル方程式 / 生物個体数 |
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| Research Abstract |
This research was intended to make a scheme for determination of the nonlinearities and/or governed equations in nonlinear problems from a viewpoint of inverse problems. Main results are as follows :
1.An inverse problem to determine an unknown velocity in two-dimensional, time-independent advection-diffusion equation from data observed at a depth-level was discussed. A procedure by which the velocity is reconstructed from the observed data is established and, as a consequence, the uniqueness of the velocity realizing the prescribed data was proved.
2.Related with the problem in (1), an inverse scattering problem to recover the potentials of an energy dependent Schrodinger equation from the scattering data was discussed. A new inversion formula was developed, by which the potentials are recovered directly through the solution of a Marchenko equation. By means of this inverse formula, a necessary and sufficient condition for a given function to be the scattering data was obtained.
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Report
(5 results)
Research Products
(20 results)
