A representation formula for solutions of equations with delay in the phase space and its applications

相空间时滞方程解的表示式及其应用

• 批准号: 13640197
• 负责人: MURAKAMI Satoru
• 金额: $ 2.18万
• 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: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640197/
• 关键词: Functional differential equations; Fading memory space; Admissibility; Variation-of-constants formula; Phase space; Solution operator; Quasi-process; Stability property; 概周期解; スペクトル; 線形化原理; 関数微分方程; 極限方程式; プロセス; 差分方程式; 遅れ時間

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.

首席调查员和10名研究人员研究了定性特性，以进行时间延迟，并在该主题上获得了许多结果。该主题的一部分结果的内容。以下总结了获得的部分结果的内容：对于无限尺寸的抽象功能微分方程，我们在相空间中建立了一个溶液的表示公式，以及分解的公式。该公式在对合法特性的研究中起着重要作用，因为人们可以使用公式将无限维方程的研究减少到有限尺寸方程的研究中。实际上，通过应用公式，我们建立了一些功能空间的可接受性和Massera类型的结果，结果几乎存在于线性功能微分方程的几乎周期性解决方案。此外，我们为非线性功能微分方程建立了一些局部不变流形，并通过线性化方程将结果应用于某些稳定性问题。此外，对于渐近周期性的功能微分方程，我们通过限制方程研究了渐近上几乎是周期性解决方案的存在。

项目成果

Yoshiyuki Hino: "Quasi-processes and slabilities in functional differential eguations"Nonlinear Anal.. 47. 4025-4036 (2001)

Yoshiyuki Hino：“泛函微分方程中的拟过程和稳定性”非线性分析.. 47. 4025-4036 (2001)

Kenichi Yoshida: "Accurate elements and super-primitive elements over Rings"Journal of Algebra. 245. 370-394 (2001)

吉田健一：“环上的精确元素和超原始元素”代数杂志。

Satoru Murakami., Nguyen V.Minh.: "Some invariant manifolds for abstract functional differential equations and linearized stabilities"Vietnam J. Math.. (in press).

Satoru Murakami.、Nguyen V.Minh.：“抽象函数微分方程和线性稳定性的一些不变流形”Vietnam J. Math..（出版中）。

Yoshiyuki Hino., and Satoru Murakami.: "Limiting equations and some stability properties for asymptotically almost periodic functional differential equations with infinite delay"Tohoku Math. Journal. 54. 239-257 (2002)

Yoshiyuki Hino. 和 Satoru Murakami.：“具有无限延迟的渐近几乎周期函数微分方程的极限方程和一些稳定性性质”东北数学。

Yoshiyuki Hino: "Decomposition of variation of constants formula for abstract functional differential equations"Funkcial. Ekvac.. 45・3. 341-372 (2002)

日野义行：“抽象泛函微分方程的变分公式的分解”Funkcial.. 45・3（2002）。