Differential Equations and Nonlinear Mechanics

A Note on Wave Equation and Convolutions

Adem Kiliçman and Hassan Eltayeb

Full-text: Open access


We study the first-order nonhomogenous wave equation. We extend the convolution theorem into a general case with a double convolution as the nonhomogenous term. The uniqueness and continuity of the solution are proved and we provide some examples in order to validate our results.

Article information

Differ. Equ. Nonlinear Mech., Volume 2007 (2007), Article ID 049251, 13 pages.

Received: 27 March 2007
Accepted: 8 November 2007
First available in Project Euclid: 26 January 2017

Permanent link to this document

Digital Object Identifier

Zentralblatt MATH identifier


Kiliçman, Adem; Eltayeb, Hassan. A Note on Wave Equation and Convolutions. Differ. Equ. Nonlinear Mech. 2007 (2007), Article ID 049251, 13 pages. doi:10.1155/2007/49251. https://projecteuclid.org/euclid.ijde/1485399784

Export citation


  • G. L. Lamb Jr., Introductory Applications of Partial Differential Equations: With Emphasis on Wave Propagation and Diffusion, A Wiley-Interscience Publication, John Wiley & Sons, New York, NY, USA, 1995. MR1322050
  • T. Myint-U, Partial Differential Equations of Mathematical Physics, North-Holland, New York, NY, USA, 2nd edition, 1980. MR564656
  • C. Constanda, Solution Techniques for Elementary Partial Differential Equations, Chapman & Hall/CRC Mathematics, Chapman & Hall, Boca Raton, Fla, USA, 2002. MR1910694
  • D. G. Duffy, Transform Methods for Solving Partial Differential Equations, Chapman & Hall, 2nd edition, 2004. MR2087015
  • \rcommentComment on ref. [5?]: We changed the authors names according to the MathSciNet database. Please check. V. A. Ditkin and A. P. Prudnikov, Operational Calculus in Two Variables and Its Applications, vol. 24 of International Series of Monographs on Pure and Applied Mathematics, Pergamon Press, New York, NY, USA, 1962. MR0138957
  • J. L. Schiff, The Laplace Transform: Theory and Applications, Undergraduate Texts in Mathematics, Springer, New York, NY, USA, 1999. MR1716143