THE GOURSAT PROBLEM FOR THE PARTIAL DIFFERENTIAL EQUATION UXYZ EQUALS F: A MIRAGE,

Abstract

A typical boundary value problem for the hyperbolic equation consists in prescribing the unknown function u(x,y) along two plane curves. This so called Goursat problem, under suitable hypotheses, is known to possess always a classical solution. However, it it shown here, by means of a simple example, that the Goursat problem for the partial differential equation which consists of prescribing the unknown function u(x,y,z) on three surfaces, does not, in general, possess a classical solution. (Author)

Document Details

Document Type
Technical Report
Publication Date
Mar 02, 1964
Accession Number
AD0437155

Entities

People

  • J. B. Diaz
  • Sherwood C. Chu

Organizations

  • Naval Ordnance Laboratory

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Differential Equations
  • Equations
  • Hypotheses
  • Mathematical Analysis
  • Partial Differential Equations

Fields of Study

  • Mathematics

Readers

  • Applied Combinatorial Optimization and Logic Circuit Design.
  • Calculus or Mathematical Analysis