Scattering theory for the elastic surface waves

点击翻译按钮获取中文摘要

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