Development of representation of elastic waves and investigation of their fundamental properties

弹性波表示的发展及其基本特性的研究

• 批准号: 21540161
• 负责人: SOGA Hideo
• 金额: $ 2.58万
• 依托单位: Ibaraki University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540161/
• 关键词: 関数方程式; 弾性方程式; 偏微分方程式; 逆問題; 散乱波; 弾性波動方程式; 散乱問題; 複素積分

The purpose in this research is the following : (1) to develop a new representation of elastic waves and to apply this to inverse problems;(2) to investigate fundamental properties of elastic waves connected with the inverse problems.The above (1) is an attempt to develop a primitive idea obtained previously into a detailed form. Although we have encountered an unexpected serious difficulty in this attempt, we succeed finally in proving the conjectured conclusion, and moreover make relation clear between the obtained representation and the known ones. Also we obtain an algorithm for an inverse problem to measure pre-stress from data of surface waves (Rayleigh waves) expressed by the representation. This is based on a formula which shows how the pre-stress depends on the velocity of the Rayleigh wave.Concerning the above (2), we get new pieces of knowledge about the energy of waves. The one is verification that the energy propagates essentially along the characteristics. The other is precise estimation for influence of the dissipative terms to the energy decay. We show also the representation in (1) is useful to prove the Huygens principle for more extensive classes than previously known. Further, we have tried to prove the unique continuation property for the general elastic equation, as was planned, and get an idea for the proof. However, we do not accomplish this proof expected first.

这项研究的目的是：（1）开发弹性波的新表示，并将其应用于反问题；（2）研究与反相关问题相关的弹性波的基本特性。上述（1）是一种试图发展先前获得的原始思想，先前获得的原始思想。尽管我们在这次尝试中遇到了意外的严重困难，但我们最终成功地证明了猜想的结论，此外，在获得的代表和已知的表述之间的关系清楚了。同样，我们还获得了一个反问题的算法，以测量从表示形式表达的表面波（瑞利波）数据的预压力。这是基于一个公式，该公式显示了预压力如何取决于雷利波的速度。牢记上述（2），我们获得了有关波浪能量的新知识。一个是验证能量基本上沿特征传播的验证。另一个是耗散术语对能量衰减的影响的精确估计。我们还显示（1）中的表示形式可用于证明与以前已知的更广泛类别的Huygens原理。此外，我们试图通过计划来证明通用弹性方程的独特延续属性，并有一个想法。但是，我们没有首先完成此证明。

项目成果

Perturbation of phase velocity of Rayleigh waves in pre-stressed anisotropic media with orthorhombic principal part

• DOI: 10.1177/1081286512438882
• 发表时间: 2013-05
• 期刊: Mathematics and Mechanics of Solids
• 影响因子: 2.6
• 作者: Kazumi Tanuma;C. Man;Wenwen Du

Cauchy積分を使った弾性波の漸近展開

使用柯西积分的弹性波渐近展开

• 发表时间: 2011
• 作者: 井上学;石村直之;中村正彰;M. Kawashita and K. Suzuki;K. Saito;Asao Arai;曽我日出夫
• 通讯作者: 曽我日出夫

Local energy decay for wave equations in exterior domains with regular or fast decaying dissipations

具有规则或快速衰减耗散的外部域中波动方程的局部能量衰减

• 发表时间: 2011
• 期刊: SUT Journal of Mathematics
• 作者: 畑沙緒里;杉江実郎;杉江実郎;Miwako Mishima;Ryo Ikehata;Hiroyasu Mizuguchi;N. NAWATA and Y. WATATANI;Masakazu Jimbo;杉江実郎;M. Kawashita and K. Suzuki
• 通讯作者: M. Kawashita and K. Suzuki

Weighted energy estimates for wave equations in exterior domains

外部域波动方程的加权能量估计

• 期刊: orum Math (掲載決定)
• 作者: M. Kawashita;H. Sugimoto
• 通讯作者: H. Sugimoto