4. The Wave Equation

  1. Peter V. O'Neil

Published Online: 24 OCT 2011

DOI: 10.1002/9781118032350.ch4

Beginning Partial Differential Equations, Second Edition

Beginning Partial Differential Equations, Second Edition

How to Cite

O'Neil, P. V. (2008) The Wave Equation, in Beginning Partial Differential Equations, Second Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118032350.ch4

Publication History

  1. Published Online: 24 OCT 2011
  2. Published Print: 20 MAR 2008

ISBN Information

Print ISBN: 9780470133903

Online ISBN: 9781118032350

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Keywords:

  • Cauchy problem;
  • wave equation;
  • Fourier integral;
  • two space dimensions;
  • Kirchhoff-Poisson solution

Summary

This chapter contains sections titled:

  • d'Alembert Solution of the Cauchy Problem

  • d'Alembert's Solution as a Sum of Waves

  • The Characteristic Triangle

  • The Wave Equation on a Half-Line

  • A Half-Line with Moving End

  • A Nonhomogeneous Problem on the Real Line

  • A General Problem on a Closed Interval

  • Fourier Series Solutions on a Closed Interval

  • A Nonhomogeneous Problem on a Closed Interval

  • The Cauchy Problem by Fourier Integral

  • A Wave Equation in Two Space Dimensions

  • The Kirchhoff-Poisson Solution

  • Hadamard's Method of Descent