International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 4, Pages 835-845
doi:10.1155/S0161171299228359
A boundary value problem for the wave equation
Department of Mathematics, Western Kentucky University, Bowling Green 42101, Kentucky, USA
Received 2 March 1998; Revised 18 August 1998
Copyright © 1999 Nezam Iraniparast. 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
Traditionally, boundary value problems have been studied for elliptic differential equations. The mathematical systems described in these cases turn out to be “well posed”. However, it is also important, both mathematically and physically, to investigate the question of boundary value problems for hyperbolic partial differential equations. In this regard, prescribing data along characteristics as formulated by Kalmenov [5] is of special interest. The most recent works in this area have resulted in a number of interesting discoveries [3, 4, 5, 7, 8]. Our aim here is to extend some of these results to a more general domain which includes the characteristics of the underlying wave equation as a part of its boundary.