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

基本信息

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

项目摘要

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.

首席研究员和五名研究人员研究了功能微分方程，Integrodiffentifence方程和Volterra差异方程的溶液的定性特性，这些方程是典型的方程式延迟的方程式，并在以下引用的主题上获得了许多结果。对于具有积分内核的线性集成差异方程，我们表征了零解的均匀渐近稳定性特性，其特征运算符的频谱分布以及wellas的分解性。作为结果的应用，对于几乎周期性扰动的方程式，我们获得了几乎周期性解决方案的足够条件，并分析了几乎周期性解决方案的光谱。此外，将方法应用于Volterra差异方程，我们获得了具有分段连续延迟的部分微分方程解的稳定性属性。2。使用延迟的线性方程中的相位空间中的变体公式，我们确定了某些非线性方程的不变歧管（例如局部稳定歧管，局部中心歧管等）的存在，并将结果应用于该结果，并将结果应用于该结果稳定问题。同样，通过一些更好的考虑，我们研究了不变流形的平稳性。3。对于与扰动的线性功能差方程，我们通过将相空间分解为稳定子空间的直接总和和不稳定的歧管，并通过溶液操作员的频谱分析来研究解决方案的渐近行为，并获得了Perron的扩展定理的普通微分方程。