Fundamental Research and Applied Numerical Analysis in Partial Differential Equations and Functional Partial Differential Equations

偏微分方程和泛函偏微分方程的基础研究和应用数值分析

基本信息

批准号：
09640163
负责人：
NAITO Toshiki
金额：
$ 1.98万
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：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

项目摘要

1. The property of Semi-Fredholm operators are effectively applied to the existence of periodic solutions of linear, nonhomogeneous functional differential equations described by the noncompact operators. A formula of generators is found for the solution semigroups of evolution equations with infinite delay on the general phase space. It is applied to the study of the spectrum, eigenfunctions of the semigroup, as well as to the study of stability.2. The flow satisfying Kutta condition can be computed numerically as precisely as possible through a finite element computation of stream function of the velocity field using the transpearent non local boundary conditions imposed on artificial boundaries suitably introduced.3. The vibration and wave propagation phenomena are studied for the following themes : Proposal of perturbation method for structural-acoustic coupled vibration problem and its justification : Proposal of the iteration method for the Helmholtz equation based on the domain decomposition technique and proof of its efficiency : Consideration of the relation between inf-sup condition and spectral pollution. The equation is derived for the vibration of a elastic string in. 3-dimensional, and its certain justification is shown.4. A convergent finite element scheme for advection equations of convection equations or convection equations is proposed. The error order estimates which is best possible is proved. The scheme is successfully applied to an advection equation for the densities in the density dependent Stokes equations.5. Existence and regularity for a solution of the evolution problem associated to p-harmonic maps is established if the target manifold has a non-positive sectional curvature.

1。半芬霍尔姆运算符的性质有效地应用于非稳定运算符所描述的线性，非均匀功能微分方程的周期性解决方案。对于一般相空间上无限延迟的进化方程的溶液半群，发现了发电机公式。它适用于对半群的光谱，特征函数以及稳定性研究的研究。2。满足kutta条件的流量可以通过使用适当引入人造边界的跨性别非局部边界条件来精确地计算数值来精确地计算速度场的流函数的有限元计算。3。 The vibration and wave propagation phenomena are studied for the following themes : Proposal of perturbation method for structural-acoustic coupled vibration problem and its justification : Proposal of the iteration method for the Helmholtz equation based on the domain decomposition technique and proof of its efficiency : Consideration of the relation between inf-sup condition and spectral pollution.该方程是为3维弹性字符串的振动得出的，并显示其一定的理由。4。提出了用于对流方程或对流方程的对流方程的收敛有限元方案。错误顺序估算最好的估算已证明。该方案成功应用于密度依赖性Stokes方程中密度的对流方程5。如果目标歧管具有非阳性的截面曲率，则建立了与P谐波图相关的进化问题解决方案的存在和规律性。