2006 Fiscal Year Final Research Report Summary
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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| Keywords | energy dependent scattering / inverse scattering problem / inverse problem / Schrodinger equation / Marchenko equation / potentials |
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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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