Harmonic Analysis and Numerical Analysis on Functional Defferential Equations and Partial Differential Equations

泛函微分方程和偏微分方程的调和分析和数值分析

基本信息

批准号：
11640155
负责人：
NAITO Toshiki
金额：
$ 2.3万
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：
1999
资助国家：
日本
起止时间：
1999 至 2001
项目状态：
已结题

项目摘要

1. The results on the analytic investigation of solution spaces, stability, existence of peridic(P-) or almost periodic(AP-) solutions in functional, partial or stochastic differential equations(DE's) : We studied the Fourier-Carleman spectrum of bounded solutions of linear DE's. Main result are decompositions of bounded solutions corresponding to the separation of spectrum, its application to the existence of P- or AP-solutions and admissiblility of function spaces. Difference equations are treated similary. Fundamental results are given on the existence and uniqueness of solutions to functional differential equations (FDE's) in Banach spaces. The spectral theory of solution semigroups of linear FDE's are applied to stability and existence of P-solutions. A new variation-of-constants formula for FDE's are established on the abstract phase space; the formula are shown to be effective on the decomposition of the phase space and the existence of P- or AP solutions.2. The results on the numerical analysis on the example of concrete applications and the development of the technique of numerical computation: About the finite element method(FEM) on 2 dimensional perfect fluid around a wing, we studied the numerical construction of conformal function of a wing by using the results on FEM to the discrite version of Laplace problem in the interior of a disk. About the scattering problem in unbounded region, we studied the numerical solving manner by using 'the domain decompositon method as well as the fictitious domain method. Among them we obtained a new view of numerical treatments of Dirichlet-Neumann problem. Including the FEM approximation of mixed type to Poisson equation, we observed the importance of the essential spectrum in the study of FEM.

1。在功能，部分或随机微分方程（DE）中，对解决方案空间，稳定性，稳定性（P-）或几乎周期性（AP-）溶液的分析结果的结果：我们研究了线性DE的有界求解溶液的傅立叶 - 手机谱。主要结果是对应于频谱分离的有界溶液的分解，其应用于p-或ap溶解的存在以及函数空间的典礼性。差异方程式相似。基本结果是关于Banach空间中功能微分方程（FDE）的解决方案的存在和独特性的基本结果。线性FDE的溶液半群的光谱理论应用于p-溶液的稳定性和存在。在抽象相空间上建立了一个新的FDE代理公式的变化。该公式被证明对相空间的分解和P-或AP溶液的存在有效2。关于混凝土应用的示例的数值分析的结果和数值计算技术的开发：关于机翼周围2尺寸完美液体的有限元方法（FEM），我们通过使用fem的结果来实现fem的结果来确定disk内部的lap裂问题，研究了机翼的保形功能的数值结构。关于无界区域中的散射问题，我们使用“域分解方法以及虚拟域方法研究了数值解决方式。其中，我们获得了Dirichlet-Neumann问题的数值治疗方法的新观点。包括混合类型与泊松方程的fem近似，我们观察到基本频谱在研究中的重要性。