| Project/Area Number |
09640156
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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 |
解析学
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| Research Institution | CHIBA UNIVERSITY |
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Principal Investigator |
HINO Yoshiyuki FACULTY OF SCIENCES,PROFESSOR, 理学部, 教授 (70004405)
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| Co-Investigator(Kenkyū-buntansha) |
OKADA Yasunori FACULTY OF SCIENCES,ASSISTANT PROFESSOR, 理学部, 助教授 (60224028)
NAGISA Masaru FACULTY OF SCIENCES,ASSISTANT PROFESSOR, 理学部, 助教授 (50189172)
KUGA Ken-ichi FACULTY OF SCIENCES,ASSISTANT PROFESSOR, 理学部, 助教授 (30186374)
ISHIMURA Ryuichi FACULTY OF SCIENCES,ASSISTANT PROFESSOR, 理学部, 助教授 (10127970)
INABA Takashi FACULTY OF SCIENCES,PROFESSOR, 理学部, 教授 (40125901)
筒井 亨 千葉大学, 理学部, 助手 (00197732)
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| Project Period (FY) |
1997 – 1998
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| Project Status |
Completed (Fiscal Year 1998)
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| Budget Amount *help |
¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 1998: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 1997: ¥1,900,000 (Direct Cost: ¥1,900,000)
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| Keywords | process / functional differential Egs / skew produt flow / stability / almost periodic function / 極限方程式 |
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| Research Abstract |
Let B = B((-*, 0] ; X), where X is a complete metric space. Consider functional differential equations with infinite delay
du/dt = AIOTA(t) + L(t, IOTA_t),
where A is an infinitesimal generator of a compact semigroup of bounded lineat operators and IOTA_t is an element of B defined by IOTA_t (s) =IOTA_t (t + s), s epsilon (-*, 0).
This phase space has two types, that is, one is a uniform fading memory space and the other is a fading memory space. Furthermore, if we consider an evolution equations which is a genaralization of partial differential equations, above equation must be considered a functional partial differential equation with infinite delay. In this report, we have the followings :
(i) Stability theoris are characterized by processes. We have a new concept of process which is a generalization of processes and we called it a quasi-process.
(ii) Nonlinear oscillations are characterized by processes. In particular, the existence of an almost periodic integral of almost periodic processes is given.
Inaba has given an example of a flow on a non-compact surface without minimal set. This result has given important informations to solve a problem (ii).
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