2002 Fiscal Year Final Research Report Summary
A representation formula for solutions of equations with delay in the phase space and its applications
| Project/Area Number |
13640197
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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) |
TAKENAKA Shigeo Okayama University of Science, Department of Applied Mathematics, Professor, 理学部, 教授 (80022680)
YOSHIDA Kenichi Okayama University of Science, Department of Applied Mathematics, Professor, 理学部, 教授 (60028264)
HAMAYA Yoshihiro Okayama University of Science, Department of Information Science, Associated Professor, 総合情報学部, 助教授 (40228549)
SHIMENO Nobukazu Okayama University of Science, Department of Applied Mathematics, Associated Professor, 理学部, 助教授 (60254140)
KURIBAYASHI Katsuhiko Okayama University of Science, Department of Applied Mathematics, Associated Professor, 理学部, 助教授 (40249751)
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| Project Period (FY) |
2001 – 2002
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| Keywords | Functional differential equations / Fading memory space / Admissibility / Variation-of-constants formula / Phase space / Solution operator / Quasi-process / Stability property |
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| Research Abstract |
Head investigator and 10 investigators studied qualitative properties for equations with time delay, and obtained many results on the subject. The contents of a part of results on the subject. The contents of a part of results obtained are summarized in the following:
For an abstract functional differential equation which is the one of infinite dimension, we established a representation formula of solutions in the phase space, together with the decomposed formula. The formula plays an important role in the study of qualitive properties, because one can reduce the study of infinite dimensional equations to the study of finite dimensional equations by using the formula. Indeed, by applying the formula we established some results on the admissibility of some function spaces and Massera's type results on the existence of almost periodic solutions for linear functional differential equations. Also, we established some local invariant manifolds for nonlinear functional differential equations, and applied the results to some stability problems via linearized equations. Furthermore, for asymptotically almost periodic functional differential equations we studied the existence of asymptotically almost periodic solutions by means of limiting equations.
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