2000 Fiscal Year Final Research Report Summary
Spectral analysis of an operator associated with equations with time delay
| Project/Area Number |
11640191
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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 | Okayama University of Science |
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Principal Investigator |
MURAKAMI Satoru Okayama University of Science, Department of Applied Mathematics, Professor, 理学部, 教授 (40123963)
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| Co-Investigator(Kenkyū-buntansha) |
NAKAMURA Tadashi Okayama University of Science, Department of Mathematical Information Science, Professor, 総合情報学部, 教授 (20069074)
YOSHIDA Kenich Okayama University of Science, Department of Applied Mathematics, Professor, 理学部, 教授 (60028264)
HAMAYA Yoshihiro Okayama University of Science, Department of Mathematical Information Science, Lecturer, 総合情報学部, 講師 (40228549)
WATANABE Hisao Okayama University of Science, Department of Applied Mathematics, Professor, 理学部, 教授 (40037677)
TAKENAKA Shigeo Okayama University of Science, Department of Applied Mathematics, Professor, 理学部, 教授 (80022680)
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| Project Period (FY) |
1999 – 2000
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| Keywords | Functional differential equations / Functional difference equations / Admissibility / Variation-of-constants formula / Phase space / Asymptotic equivalence / Volterra systems / Stability property |
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| Research Abstract |
Head investigator and 8 investigators studied some properties of solutions in equations with time delay, and obtained many results on the subject. The contents of a part of results obtained are summarized in the following :
First we analyzed some prperties of spectrum of the operator associated with functional difference equations and functional differential equations which are typical ones as equations with time delay. As applications of the result, we investigated the asymptotic equivalence of solutions and admissibility of some function spaces, and obtained some results on the subjects. These results are almost best possible ones in equations of finite dimension.
Next we treated an abstract functional differential equation which is the one of infinite dimension and established a variation-of-constants formula which represents the segment of solutions in the phase space. This formula is crucial in the study of qualitative properties, because one can reduce the study of inifinite dimensional equations to the study of finite dimensional equations by using the formula. Indeed, by using the formula we established a result in admissibility theory for infinite dimensional equations.
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Research Products
(12 results)
