2001 Fiscal Year Final Research Report Summary
Nonlinear Inverse Problems and Singular Integral Equations
| Project/Area Number |
10440038
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 Fisheries |
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Principal Investigator |
KAMIMURA Yutaka Tokyo University of Fisheries, Dept. of Fisheries, Professor, 水産学部, 教授 (50134854)
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| Co-Investigator(Kenkyū-buntansha) |
HINO Yoshiyuki Chiba University, Dept. of Science, Professor, 理学部, 教授 (70004405)
SHIOTANI Nobuhira Tokyo University of Fisheries, Dept. of Fisheries, Professor, 水産学部, 教授 (30087415)
TSUBOI Kenji Tokyo University of Fisheries, Dept. of Fisheries, Associate Professor, 水産学部, 助教授 (50180047)
IWASAKI Katsunori Kyushu University, Faculty of Mathematics, Professor, 数理学研究科, 教授 (00176538)
HARAOKA Yoshishige Kumamoto Univeristy, Dept. of Science, Associate Professor, 理学部, 助教授 (30208665)
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| Project Period (FY) |
1998 – 2001
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| Keywords | nonlinear inverse problem / singular integral equation / Wiener-Hopf equation / inverse bifurcation problem / mathematical ecology / population dynamics / conductivity identification |
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| Research Abstract |
Several nonlinear inverse problems in mathematical sciences are discussed : a friction coefficient identification problem, a nonlinearity identification problem in nonlinear oscillations, a time-dependent thermal conductivity identification problem, inverse bifurcation problem in mathematical ecology (nonlinear reaction kinetics identification problem in a diffusional model of population dynamics from the relation between growth rates and certain central densities of population distributions). A certain class of singular integral equations plays a principal role in our mathematical analysis of the inverse problems ; some existence results of the solutions to the integral equations are established and applied to the inverse problems.
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