Study of partial differential equations appearing in continuum mechanics and utlization of mathematical softwares

连续介质力学中偏微分方程的研究及数学软件的应用

• 批准号: 12640159
• 负责人: ITO Hiroya
• 金额: $ 2.24万
• 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: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640159/
• 关键词: slip boundary condition; Korn's inequality; positively; elastic wave equation; Mathematica; Mobius band; ベクトル値関数; Rayleigh波; 弾性体方程式; 圧電体方程式; 層状媒質; Barnett-Lotheテンソル; 亀裂進展問題

Main results obtained in the period are as follows :1.Korn-type inequalities for. vector fields tangent to the boundary have been studied. Important contributions are : (1) a class of singular domains on which Korn-type inequalities hold for vector fields tangent to the boundary has been proposed. (2) Korn-type inequalities for energy integral of isotropic elasticity with some degeneracy of strong convexity condition was investigated.2.A sufficient condition imposed on the coefficients for the static energy integral to be positive for vector-valued functions on any bounded Lipschitz domain was studied. Now the corresponding necessary condition is now being studied.3.Eigenvalue problem for the reduced wave equation of isotropic elasticity on a slab has been investigated in detail.4.We utilized the mathematical software "Mathematica" to realize Mobius band in Mathmatica' using narrow strip of flat paper with the aid of three slender circular cylinders.

主要结果如下：1.关于.已经研究了与边界相切的矢量场。重要贡献包括：（1）提出了一类奇异域，其上的Korn型不等式对与边界相切的向量场成立。(2)研究了各向同性弹性力学在强凸性条件退化下能量积分的Korn型不等式。2.研究了有界Lipschitz域上向量值函数的静力能量积分系数为正的充分条件。3.详细研究了板上各向同性弹性力学约化波动方程的本征值问题。4.利用数学软件Mathematica，利用三个细长圆柱和一张窄扁纸实现了Mathematica中的Mobius带。