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.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 2002
Accession Number
ADP013930

Entities

People

  • Alla A. Gousenkova

Organizations

  • Kazan Federal University

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Applied Mathematics
  • Boundaries
  • Boundary Value Problems
  • Differential Equations
  • Diffraction
  • Displacement
  • Electromagnetism
  • Electronic Mail
  • Equations
  • Formulas (Mathematics)
  • Fourier Transformation
  • Helmholtz Equations
  • Integral Equations
  • Integrals
  • Linear Algebraic Equations
  • Technical Information Centers

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Materials Science and Engineering.

Technology Areas

  • Space