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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Fredholm算子的性质被有效地应用于由非紧算子描述的线性非齐次泛函微分方程周期解的存在性。给出了一般相空间上无穷时滞发展方程解半群的生成元公式。它被应用于半群的谱、特征函数以及稳定性的研究.通过在人工边界上适当引入瞬态非局部边界条件，对速度场流函数进行有限元计算，可以尽可能精确地数值计算满足库塔条件的流动.振动和波的传播现象进行了研究，为以下主题：结构-声耦合振动问题的摄动方法的建议及其理由：Helmholtz方程的迭代方法的建议基于区域分解技术和证明其效率：考虑inf-sup条件和频谱污染之间的关系。本文推导了弹性弦振动的方程。3维的，并显示其一定的理由。对对流方程或对流方程的对流方程提出了一个收敛的有限元格式。证明了最佳可能的误差阶估计。将该格式成功地应用于与密度相关的Stokes方程中的密度对流方程.在目标流形具有非正截面曲率的条件下，证明了p-调和映射演化问题解的存在性和正则性。