Scattering theory for the elastic surface waves

弹性表面波的散射理论

• 批准号: 14540176
• 负责人: KAWASHITA Mishio
• 金额: $ 2.18万
• 依托单位: HIROSHIMA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540176/
• 关键词: Surface waves; Scattering theory; Rayleigh waves; Lax-Phillips; Wilcox; wave equations; Lax-Phillps

The subject of the research is to clarify whether the surface waves propagating on boundaries of elastic medium can be regarded in the framework of the scattering theory or not. We obtain the following results on the problems about formulations of mathematical scattering theory suitable to analyzing the surface waves(1) We can construct a formulation of the scattering theory of Lax and Phillips type(2) We can find the diffences of scattering phenomena between the one for body waves and the one for surface waves(3) For formulations of scattering theories with respect to hyprebolic problems, it was known that there were two differnt types (Wilcox type and Lax-Phillips type). We can show that those two types are equivalent each other using an abstract frameworkFrom those results we can compair the scatteing theories obtained in the research and the previous onesOur next concern is to clarify the properties of the scattered surface waves. For the purpose, we obtain the following results(4) For surface waves propagating on the flat boundaries, How energies of them propagate(5) A low frequency analysis of stationary waves on perturbed boundaryThese results are expected to a basis on the further study of the properties of the surface waves

本文研究的问题是：在弹性介质边界上传播的表面波是否可以用散射理论来处理。本文对适用于分析表面波的数学散射理论的公式问题，得到了如下结果：（1）可以构造Lax和菲利普斯型散射理论的公式;（2）可以发现体波散射理论与表面波散射理论的区别;（3）对于双曲问题的散射理论公式，已知有两种不同的类型（Wilcox型和Lax-Phillips型）。我们可以使用抽象框架来证明这两种类型是相互等效的。从这些结果中，我们可以将研究中获得的散射理论与之前的理论进行比较。我们的下一个问题是澄清散射表面波的性质。为此，我们得到了下列结果：（4）对于在平坦边界上传播的表面波，表面波的能量如何传播;（5）扰动边界上驻波的低频分析这些结果可望为进一步研究表面波的性质奠定基础

项目成果

盛田 健彦: "測度論と実解析の基礎"培風館(発行予定). 296

森田武彦：《测度论与实分析基础》百风馆（待出版）296。

M.Kawashita, H.Nakazawa, H.Soga: "Non decay of the total energy for the wave equation with the dissipative term of spatial anisotropy"Nagoya J.Math.. (in press).

M.Kawashita、H.Nakazawa、H.Soga：“具有空间各向异性耗散项的波动方程总能量的非衰减”Nagoya J.Math..（出版中）。

M.Kawashita: "On global solutions of Cauchy problems for compressible Navier-Stokes equations"Nonlinear Analy.. 48・2. 1087-1105 (2002)

M.Kawashita：“关于可压缩纳维-斯托克斯方程的柯西问题的全局解”非线性分析.. 1087-1105 (2002)

R.Ikehata: "Diffusion phenomenon for linear dissipative wave equations in unbounded domains"J.Diff.Eq.. 186-2. 633-651 (2002)

R.Ikehata：“无界域中线性耗散波方程的扩散现象”J.Diff.Eq.. 186-2。

R.Ikehata: "Fast decay of solutions for linear wave equations with dissipation localized near infinity in an exterior domain"J.Diff.Eq.. 188-2. 390-405 (2003)

R.Ikehata：“外部域中耗散局域于无穷大的线性波动方程解的快速衰减”J.Diff.Eq.. 188-2。