Differential Equations and Nonlinear Mechanics
Volume 2007 (2007), Article ID 49251, 13 pages
doi:10.1155/2007/49251
Research Article

A Note on Wave Equation and Convolutions

Adem Kılıçman and Hassan Eltayeb

Department of Mathematics, Faculty of Science and Technology, University of Malaysia Terengganu (UMT), Terengganu 21030, Kuala Terengganu, Malaysia

Received 27 March 2007; Accepted 8 November 2007

Academic Editor: Shijun Liao

Copyright © 2007 Adem Kılıçman and Hassan Eltayeb. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.