DOMAINS OF DEPENDENCE FOR MIXED PROBLEMS FOR WAVE EQUATIONS,

Abstract

The energy integral method in its usual form involving the use of the characteristic conoid is easily extended to yield a uniqueness theorem for mixed problems for the wave equation. Friedlander ('Sound pulses.' Cambridge, Cambridge Univ. Press, 1958. Proc. of the Cambridge Philosophical Society 45:395 (1949)) noted this and used it to determine the fronts of disturbances in the shadow region resulting from mixed problems with homogeneous boundary conditions. It is shown how these fronts may be used to obtain a uniqueness theorem for such mixed problems with smooth boundaries, and, thereby, domains of dependence and influence for such problems, with homogeneous boundary conditions. These domains are smaller than those obtained from the usual energy integral method referred to above and coincide with those of the solutions of several particular mixed problems.

Document Details

Document Type
Technical Report
Publication Date
Aug 12, 1963
Accession Number
AD0618990

Entities

People

  • Erich Zauderer

Organizations

  • New York University

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Differential Equations
  • Equations
  • Integrals
  • Mathematics
  • Mechanics
  • Wave Equations

Fields of Study

  • Mathematics

Readers

  • Combustion Dynamics and Shock Wave Physics.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Theoretical Analysis.