ON THE RIEMANN MATRIX OF A HYPERBOLIC SYSTEM

Abstract

Consideration is given to linear first order partial differential equations with constant coefficients, which are hyperbolic. The structure and behavior of their elementary solutions are examined. The study is confined to systems which are homogeneous of the first order in derivatives, and enables one to analyze, separately, two aspects (differential and matrix) of the operators in the differential system. The Riemann matrix (the matrix elementary solution of the system) is derived from a spherical mean of the spectral resolution of the coefficient matrix. An alternative approach, based on the convergence theory of Fourier series and integrals, is used. The relation between a first order system and the irreducible equation of higher order satisfied by certain combinations of the components is examined. The Riemann matrix is then expressed as an integral over the velocity or spectral surface related to the matrix operator.

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1961
Accession Number
AD0266871

Entities

People

  • G.f.d. Duff

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Coefficients
  • Convergence
  • Differential Equations
  • Equations
  • Fourier Series
  • Integrals
  • Mathematical Analysis
  • Mathematics
  • Partial Differential Equations
  • Real Variables

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)