2001 Fiscal Year Final Research Report Summary
QUALITATIVE THEOR OF SOLUTION OF DIFFERENTIAL EQUATIONS WITH DELAYS
| Project/Area Number |
12640155
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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 | CHIBA UNIVERSITY |
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Principal Investigator |
HINO Yoshiyuki FACULTY OF SCIENCES, CHIBA UNIVERSITY, PROFESSOR, 理学部, 教授 (70004405)
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| Co-Investigator(Kenkyū-buntansha) |
OKADA Yasunori FACULTY OF SCIENCES, CHIBA UNIVERSITY, PROFESSOR, 理学部, 助教授 (60224028)
SHIMURA Ryuichi FACULTY OF SCIENCES, CHIBA UNIVERSITY, PROFESSOR, 理学部, 教授 (10127970)
INABA Takashi GRADUATE SCHOOL OF SCIENCES, CHIBA UNIVERSITY, PROFESSOR, 大学院・自然科学研究科, 教授 (40125901)
MURAKAMI Satoru OKAYAMA UNIVERSITY SCIENCES, PROFESSOR, 理学部, 教授 (40123963)
内藤 敏機 電気通信大学, 電気通信学部, 教授 (60004446)
TSUTSUI Toru FACULTY OF SCIENCES, CHIBA UNIVERSITY, ASSISTANT (00197732)
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| Project Period (FY) |
2000 – 2001
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| Keywords | DELAY EQUATIONS / STABILITY / PERIODIC SOLUTION / ALMOST PERIODIC SOLUTION / LIMITING EQUATIONS |
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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= Au(t) + L(t, u_t),
where A is an infinitesimal generator of a compact semigroup of bounded lineat operators and u_t is an element of B defined by u_t(s) = u(t + s), s ∈ (-∞, 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 generalization of partial differential equations, above equation must be considered a functional partial differential equation with infinite delay. In this report, we have the following for the above equations.
(i) Equivalent relationship between ρ-stabilities and BC-stabilities are shown.
(ii) BC-total stability for a limiting equation implies that of the given euqation. BC-uniform asymptotic stabilituy also has the same property, under the uniqueness of the solution for the initial value problem.
(iii) BC-total stability and BC-uniform asymtotic stability implies the existence of almost periodic solution of almost periodic euquations under the assumption of the existence of a bounded solution.
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Research Products
(16 results)
