The Energy Decay of Solutions to the Initial-Boundary Value Problem for the Wave Equation in an Inhomogeneous Medium

Abstract

The paper is concerned with the decay of the energy of disturbances which are propagated according to the wave equation with variable index of refraction in the exterior of a finite star-shaped reflecting body. It is shown that the energy of the disturbance decays like some power of t to the minus 1. Certain conditions of growth and continuity are made on the index in order to insure some decay factor. The energy decay is obtained by estimating the solution of an integral equation which results when one applies the Friedrichs' 'A-B-C method' to the modified wave equation operator. Using the energy estimate with other familiar estimates, one obtains a rate of decay for the disturbance itself.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1964
Accession Number
AD0605508

Entities

People

  • B. B. Lieberman

Organizations

  • New York University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force
  • Amplitude
  • Boundary Value Problems
  • Coordinate Systems
  • Differential Equations
  • Equations
  • Four Dimensional
  • Inequalities
  • Integral Equations
  • Integrals
  • Refraction
  • Refractive Index
  • Three Dimensional
  • United States
  • United States Government
  • Wave Equations

Fields of Study

  • Mathematics
  • Physics

Readers

  • Calculus or Mathematical Analysis
  • Graph Algorithms and Convex Optimization.