| Project/Area Number |
11640155
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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 |
Basic analysis
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| Research Institution | The University of Electro-Communications |
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Principal Investigator |
NAITO Toshiki The University of Electro-Communications, Faculty of Electro-Communications, Professor, 電気通信学部, 教授 (60004446)
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| Co-Investigator(Kenkyū-buntansha) |
HINO Yoshiyuki Chiba University, Faculty of Science, Professor, 理学部, 教授 (70004405)
KATO Takeshi The University of Electro-Communications, Faculty of Electro-Communications, Professor, 電気通信学部, 教授 (30012488)
USHIJIMA Teruo The University of Electro-Communications, Faculty of Electro-Communications, Professor, 電気通信学部, 教授 (10012410)
MURAKAMI Satoru Okayama Science University, Faculty of Science, Professor, 理学部, 教授 (40123963)
FURUMOCHI Tetsuo Shimane University, Interdisciplinary Faculty of Science and Engineering, Professor, 総合理工学部, 教授 (40039128)
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| Project Period (FY) |
1999 – 2001
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| Keywords | Functional Differential Equations / Variation-of-constants Formula / Periodic Solutions / Almost Periodi Solutios / Spectrum / Finite Element Method / Perfect Fluid / Domain Decomposition |
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| Research Abstract |
1. The results on the analytic investigation of solution spaces, stability, existence of peridic(P-) or almost periodic(AP-) solutions in functional, partial or stochastic differential equations(DE's) : We studied the Fourier-Carleman spectrum of bounded solutions of linear DE's. Main result are decompositions of bounded solutions corresponding to the separation of spectrum, its application to the existence of P- or AP-solutions and admissiblility of function spaces. Difference equations are treated similary. Fundamental results are given on the existence and uniqueness of solutions to functional differential equations (FDE's) in Banach spaces. The spectral theory of solution semigroups of linear FDE's are applied to stability and existence of P-solutions. A new variation-of-constants formula for FDE's are established on the abstract phase space; the formula are shown to be effective on the decomposition of the phase space and the existence of P- or AP solutions.
2. The results on the numerical analysis on the example of concrete applications and the development of the technique of numerical computation: About the finite element method(FEM) on 2 dimensional perfect fluid around a wing, we studied the numerical construction of conformal function of a wing by using the results on FEM to the discrite version of Laplace problem in the interior of a disk. About the scattering problem in unbounded region, we studied the numerical solving manner by using 'the domain decompositon method as well as the fictitious domain method. Among them we obtained a new view of numerical treatments of Dirichlet-Neumann problem. Including the FEM approximation of mixed type to Poisson equation, we observed the importance of the essential spectrum in the study of FEM.
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