| Project/Area Number |
14540158
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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 Elector-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)
TAKASHI Kako The University of Electro-Communications, Faculty of Elector-Communications, Professor, 電気通信学部, 教授 (30012488)
USHIJIMA Teruo The University of Electro-Communications, Faculty of Elector-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, 総合理学部, 教授 (40039128)
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| Project Period (FY) |
2002 – 2003
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| Keywords | Linear Differential Equations / Linear Difference Equations / Bounded Solutions / Almost Periodic Solutions / Variation of Constants Formula / Fundamental Solution Method / Voice generation / Population Dynamics |
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| Research Abstract |
1.The existence conditions of bounded solutions of the linear differential equation with a periodic forcing function are obtained by using the difference equations. The itteration of the period solution map makes a sequence which is a solutions of a linear difference equation. The general term of this sequence is represented by the initial term, the mean of the periodic forcing function and the eigenvalues of the coefficient matrix. The boundedness and periodicity of solutions are determined completely by initial values ant the mean of the forcing functions. 2.Linear functional differential equations in a Banach space are transformed to opertor equations on the space of bounded continuous functions. The spectrum of the solutions are computed and the existence of solutions whose spectrum satisfies the period conditions are computed and the existence of solutions whose spectrum satisfies the period conditions are obtained. 3.The general variation of constants formula is completely obtain
… More
ed on the phase space for linear periodic functional differential equations. The formula is applied for the existence of periodic solutions. 4.Analytic solutions of difference equations are applied to the research in the population and environmental sciences. 5.The numerical simulation algorithm is developed based on the finite element method that reduces the radiation and scattering problem in an unbounded region into the one in a bounded region using aritificial boundary. 6.A fundamental solution method applied to reduced wave problems in the exterior domain of disc has been investigated. The case of equi-distant equally phased arrangement of source points and collocation points has been studied from the view points of both theoretical analysis and numerical experiment. 7.Pertabations of eigenvalues are studied for structural-acoustic system. Well-posedness of the Cauchy problem is studied in Gevrey class for some weakly hyperbolic equations of higher order. Fixed point theorems are applied to the stability theory of solutions of integral differential equations. Less
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