Research on Global Properties and Correlation of Solutions to Functioanl Equations and Difference Equations

函数方程和差分方程解的全局性质及相关性研究

基本信息

批准号：
14540158
负责人：
NAITO Toshiki
金额：
$ 2.62万
依托单位：
The University of Electro-Communications
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2003
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540158/
关键词：
Linear Differential Equations Linear Difference Equations Bounded Solutions Almost Periodic Solutions Variation of Constants Formula Fundamental Solution Method Voice generation Population Dynamics 周期線形微分方程式周期写像初期値問題周期解周期線形関数微分

项目摘要

1.The existence conditions of bounded solutions of the linear differential equation with a periodic forcing function are obtained by using the difference equations. The itteration of the period solution map makes a sequence which is a solutions of a linear difference equation. The general term of this sequence is represented by the initial term, the mean of the periodic forcing function and the eigenvalues of the coefficient matrix. The boundedness and periodicity of solutions are determined completely by initial values ant the mean of the forcing functions. 2.Linear functional differential equations in a Banach space are transformed to opertor equations on the space of bounded continuous functions. The spectrum of the solutions are computed and the existence of solutions whose spectrum satisfies the period conditions are computed and the existence of solutions whose spectrum satisfies the period conditions are obtained. 3.The general variation of constants formula is completely obtain … More ed on the phase space for linear periodic functional differential equations. The formula is applied for the existence of periodic solutions. 4.Analytic solutions of difference equations are applied to the research in the population and environmental sciences. 5.The numerical simulation algorithm is developed based on the finite element method that reduces the radiation and scattering problem in an unbounded region into the one in a bounded region using aritificial boundary. 6.A fundamental solution method applied to reduced wave problems in the exterior domain of disc has been investigated. The case of equi-distant equally phased arrangement of source points and collocation points has been studied from the view points of both theoretical analysis and numerical experiment. 7.Pertabations of eigenvalues are studied for structural-acoustic system. Well-posedness of the Cauchy problem is studied in Gevrey class for some weakly hyperbolic equations of higher order. Fixed point theorems are applied to the stability theory of solutions of integral differential equations. Less

1.使用差异方程可获得具有周期性强迫函数的线性微分方程有界解决方案的存在条件。周期解图的迭代是一个序列，该序列是线性差方程的解。该序列的一般项由最初项，周期性强迫函数的含义和核心矩阵的特征值表示。解决方案的界限和周期性完全由初始值ant ant决定强迫函数的含义。 2. Banach空间中的线性功能微分方程将转换为有限连续函数空间上的操作员方程。计算解决方案的光谱，并存在其频谱满足周期条件的解决方案的存在，并存在其频谱满足周期条件的溶液的存在。 3。完全获得常数公式的一般变化……在线性周期性功能微分方程的相空间上，更多的是。该公式用于周期性解决方案的存在。 4.差异方程的分析解决方案应用于人群和环境科学的研究。 5.数值模拟算法是基于最终元素方法开发的，该方法将无界区域的辐射和散射问题降低到使用弧形边界的界面区域中的辐射和散射问题。 6.已经研究了用于减少椎间盘外部领域的波浪问题的基本解决方案方法。从理论分析和数值实验的观点研究了源点和搭配点的分阶段排列的情况。 7.特征值的序列是结构性声学系统的研究。对于某些较弱的高阶双曲线方程，凯奇问题的适应性是Gevrey类中的研究。固定点定理应用于整体微分方程解的稳定性理论。较少的