Spectral analysis of an operator associated with equations with time delay

与时滞方程相关的算子的谱分析

• 批准号: 11640191
• 负责人: MURAKAMI Satoru
• 金额: $ 2.05万
• 依托单位: Okayama University of Science
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640191/
• 关键词: Functional differential equations; Functional difference equations; Admissibility; Variation-of-constants formula; Phase space; Asymptotic equivalence; Volterra systems; Stability property; 定性理論; 時間遅れ; 漸近挙動; 準プロセス; スペクトル; 周期解; 概周期解

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.

主要研究员和8名研究员研究了时滞方程解的一些性质，得到了许多结果。首先，我们分析了泛函差分方程和泛函微分方程这两类典型的时滞方程所对应的算子谱的一些性质。作为结果的应用，我们研究了一些函数空间解的渐近等价性和可容许性，得到了一些结果。这些结果在有限维方程中几乎是最好的结果。其次，我们处理了一个抽象的无穷维泛函微分方程，建立了一个常数变分公式，它表示相空间中的解段。这个公式在定性性质的研究中是至关重要的，因为利用这个公式可以将无穷维方程的研究简化为有限维方程的研究。实际上，利用这个公式，我们建立了无穷维方程容许性理论中的一个结果。

项目成果

Satoru Murakanni: "Evolution slmigroups and euoms of commuting operators a new approach to the admissibility theory of function spaces"J.Differential Equateins. 164. 240-285 (2000)

Satoru Murakanni：“通勤算子的演化 slmigroups 和 euoms 是函数空间容许理论的新方法”J.Differential Equateins。

Yoshihiro Hamaya: "On the asymptotic behavior of a diffusive epidemic model(AIDS)"Nonlinear Analysis,T.M.A.. 36. 685-696 (1999)

Yoshihiro Hamaya：“关于扩散流行病模型（艾滋病）的渐近行为”非线性分析，T.M.A.. 36. 685-696 (1999)

Yoshiyuki Hino: "A variation-of-constants formula for abstract functional differential equations in the phase space"J. Differential Equations. (発表予定).

Yoshiyuki Hino：“相空间中抽象泛函微分方程的常数变分公式”J.微分方程。

Kenichi Yoshida: "On the integral closedness of the ring R[α]∩RI[1/α]"Journal of Algebra. 216. 124-134 (1999)

Kenichi Yoshida：“论环 R[α]∩RI[1/α] 的积分闭性”代数杂志 216. 124-134 (1999)

Saber Elaydi: "Asymptotic equiralence for difference equations with infinite delay"J.Difference Equ.Appl.. 5. 1-23 (1999)

Saber Elaydi：“无限延迟差分方程的渐近等价”J.Difference Equ.Appl.. 5. 1-23 (1999)