DISPERSION RELATIONS AND MIXED BOUNDARY VALUE PROBLEMS,

Abstract

The connection between dispersion relations and the solutions of the original partial differential equations in finite systems, involving mixed boundary conditions, is discussed. To illustrate this connection, a generalized wave equation is employed, which can exhibit four common forms of dispersion relations. These four cases are examined to illustrate the modifications arising from finite system, possible misconceptions concerning dispersion relations, and the role or retarded (causal) boundary conditions in classifying instabilities. Some mathematical problems of analysis, which apparently have yet to be solved, are also noted. (Author)

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1969
Accession Number
AD0693806

Entities

People

  • E. A. Jackson

Organizations

  • University of Illinois Urbana–Champaign

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Differential Equations
  • Dispersion Relations
  • Dispersions
  • Equations
  • Instability
  • Partial Differential Equations
  • Wave Equations

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Theoretical Analysis.