THE CAUCHY PROBLEM FOR PARTIAL DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND THE METHOD OF ASCENT

Abstract

A method of ascent is used to solve the Cauchy problem for linear partial differential equations of the second order in p space variables with constant coefficients i.e., the pure wave equation, the damped wave equation, and the heat equation. This method consists of inferring the solution of the problem referred to from the well known solution of the same problem for one space variable. The commutability of repeated pf integral, the solution deduced by the method of singularities for the Cauchy problem for the damped wave equation, and the solution of singular integral equations of the Volterra type are also considered. (Author)

Document Details

Document Type
Technical Report
Publication Date
May 01, 1961
Accession Number
AD0262025

Entities

People

  • F.j. Bureau

Organizations

  • University of Liège

Tags

DTIC Thesaurus Topics

  • Boundary Value Problems
  • Cauchy Problem
  • Coefficients
  • Differential Equations
  • Equations
  • Integral Equations
  • Integrals
  • Partial Differential Equations
  • Wave Equations

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.
  • Fluid Dynamics.
  • Statistical inference.

Technology Areas

  • AI & ML
  • AI & ML - Machine Learning Algorithms
  • Space