Piecewise Continuous Solutions of Pseudoparabolic Equations in Two Space Dimensions.

Abstract

One of the principal boundary value problems in analytic function theory is the so-called Riemann boundary value problem. The simplest version of the problem requires the finding of an analytic function phi in C/Gamma, where Gamma is a closed smooth contour, and a prescribed Hoelder continuous jump is prescribed for phi across Gamma. The solution of this problem may be given in terms of a Cauchy integral. In generalized analytic, as well as generalized hyperanalytic function theory, a Cauchy-type representation exists, which suggest that the Riemann problem may be solved in a similar way. In the present work several new representations for initial value problems are obtained. An iterative scheme is presented for solving the initial-boundary value problem. These results are of interest for investigating wave motion in anisotropic, nonhomogeneous elastic materials.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1977
Accession Number
ADA046453

Entities

People

  • Heinrich Begehr
  • Robert P. Gilbert

Organizations

  • University of Delaware

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Air Force
  • Analytic Functions
  • Boundaries
  • Boundary Value Problems
  • Cauchy Problem
  • Coefficients
  • Differential Equations
  • Elastic Materials
  • Equations
  • Integral Equations
  • Integrals
  • Scientific Research

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)

Technology Areas

  • Space