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.

首席研究员和 10 名研究员研究了时滞方程的定性性质，并获得了该主题的许多结果。该主题的部分结果的内容。所得部分结果内容概括如下： 对于一个无限维的抽象泛函微分方程，我们建立了相空间解的表示式，并给出了分解式。该公式在定性性质的研究中具有重要作用，因为利用该公式可以将无限维方程的研究简化为有限维方程的研究。事实上，通过应用该公式，我们建立了一些关于某些函数空间的可接受性的结果，以及关于线性泛函微分方程的几乎周期解的存在性的 Massera 类型结果。此外，我们还建立了一些非线性泛函微分方程的局部不变流形，并通过线性化方程将结果应用于一些稳定性问题。此外，对于渐近近似周期函数微分方程，我们通过极限方程研究了渐近近似周期解的存在性。

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。

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。

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: "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）。