Formal adjoint equation for equations with time delay and its applications

时滞方程的形式伴随方程及其应用

• 批准号: 16540177
• 负责人: MURAKAMI Satoru
• 金额: $ 1.34万
• 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: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16540177/
• 关键词: Functional Differential Equations; Functional Difference Equations; Phase space; Stabilities; Almost periodic solutions; Solution operators; Variation-of-constans formula; Asymptotic behavior; スペクトル; 積分微分方程式; ボルテラ差分方程式

Head investigator and five investigators studied qualitative properties of solutions of functional differential equations, integrodifferential equations and Volterra difference equations which are typical ones of equations with delay, and obtained many results on the subject as cited below.1. For linear integrodifferential equations with integrable kernels, we characterized uniform asymptotic stability property of the zero solution in terms of the distribution of spectrum of the characteristic operator as wellas the integrability of the resolvent. As an application of the result, for equations with almost periodic perturbation we obtained a sufficient condition for the existence of almost periodic solutions, and analyzed the spectrum of the almost periodic solutions. Furthermore, applying the method to Volterra difference equations, we obtained some result on the stability property of the solution of partial differential equations with piecewise continuous delay.2. Using a variation-of-constants formula in the phase space for linear equations with delay, we established the existence of invariant manifolds (such as local stable manifold, local center manifold and so on) for some nonlinear equations, and applied the result to the stability problem. Also, through some finer considerations, we investigated the smoothness of the invariant manifolds.3. For linear functional difference equations with perturbations, we investigated the asymptotic behavior of solutions by decomposing the phase space into the direct sum of the stable subspace and the unstable manifold by means of the spectrum analysis of the solution operator, and obtained an extension of the Perron theorem for ordinary differential equations.

主要研究员和五名研究员研究了时滞方程中典型的泛函微分方程、积分微分方程和沃尔泰拉差分方程的解的定性性质，并获得了以下所述的许多结果。1.对于具有可积核的线性积分微分方程，利用特征算子的谱分布和预解式的可积性，刻画了零解的一致渐近稳定性.作为结果的应用，我们得到了具有概周期扰动的方程概周期解存在的一个充分条件，并分析了概周期解的谱.进一步，将该方法应用于沃尔泰拉差分方程，得到了关于分段连续时滞偏微分方程解的稳定性的一些结果.利用相空间中线性时滞方程的常数变分公式，建立了某些非线性方程的不变流形（如局部稳定流形、局部中心流形等）的存在性，并将结果应用于稳定性问题.同时，通过一些更精细的考虑，我们研究了不变流形的光滑性.对于带扰动的线性泛函差分方程，通过解算子的谱分析，将相空间分解为稳定子空间与不稳定流形的直和，研究了其解的渐近性态，推广了常微分方程的Perron定理.

项目成果

Volterra difference equations on a Banach space and abstract differential equations with piecewise continuous delays

Banach 空间上的 Volterra 差分方程和具有分段连续时滞的抽象微分方程

• 发表时间: 2004
• 期刊: Japanese Journal of Mathematics 30-2
• 作者: T.Furumochi;S.Murakami;Y.Nagabuchi
• 通讯作者: Y.Nagabuchi

Some Invariant Manifolds for Functional Difference Equations with Infinite Delay

• DOI: 10.1080/10236190410001685021
• 发表时间: 2004-06
• 期刊: Journal of Difference Equations and Applications
• 影响因子: 1.1
• 作者: Hideaki Matsunaga *a;S. Murakami

Stability properties and asymptoticalmost periodicity for linear Volterra difference equations in a Banach space

Banach 空间中线性 Volterra 差分方程的稳定性性质和渐近周期性

• 发表时间: 2005
• 期刊: Japanese J.Mathematics vol.31
• 作者: Satoru Murakami;Yutaka Nagabuchi
• 通讯作者: Yutaka Nagabuchi

Asymptotic behavior of solutions of functional difference equations

函数差分方程解的渐近行为

• 发表时间: 2005
• 期刊: Journal of Mathematical Analysis and Applications 305
• 作者: Hideaki Matsunaga;Satoru Murakami
• 通讯作者: Satoru Murakami

Stability properties and asymptotic almost periodicity for linear Volterra difference equations in Banach pace

Banach 步调中线性 Volterra 差分方程的稳定性性质和渐近近似周期性

• 期刊: Japanese Journal of Mathematics (発表予定)
• 作者: Toshiki Naito;J.S.Shin;Satoru Murakami;Pham A.Ngoc;Satoshi Tanaka;Yoshiyuki Hino;Satoru Murakami
• 通讯作者: Satoru Murakami