Mathematical Methods in Some Diffraction Problems for Domains with Defects
Abstract
Mathematical methods in diffraction problems for elastic time-harmonic waves on defects are considered. It is assumed that the body forces are absent and the defect may be disposed on the plane in the homogeneous isotropic space or on the media interface of two homogeneous isotropic half-spaces. It is obtained systems of singular integral equations equivalent to the problems. Considered mathematical methods may be useful for solving some form researched in 1 diffraction problems for electromagnetic time-harmonic waves on defects. Some approaches to elastodynamic problems in the case of the anisotropic elastic medium are considered too. It is get analogues of the Lopatinskii condition and boundary conditions of an elliptic boundary value problem in the half-space. It is shown that both approaches are equivalent. To solve these problems the classes of outgoing from a plane solutions are introduced. The Fourier transformation in the class of generalized functions of the slow growth at infinity and presentations of solutions of the problems by potential functions are used.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 2002
- Accession Number
- ADP013930
Entities
People
- Alla A. Gousenkova
Organizations
- Kazan Federal University