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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 891078, 11 pages
http://dx.doi.org/10.1155/2012/891078
Research Article

The Inverse Problem for a General Class of Multidimensional Hyperbolic Equations

1Department of Economics and CRED, University of Namur (FUNDP), 5000 Namur, Belgium
2ECARES, Université libre de Bruxelles, 1050 Bruxelles, Belgium
3Department of Mathematics, Aktobe State University, 030000 Aktobe, Kazakhstan

Received 1 July 2011; Accepted 4 August 2011

Academic Editor: Carlo Cattani

Copyright © 2012 Gani Aldashev and Serik A. Aldashev. 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

Inverse problems for hyperbolic equations are found in geophysical prospecting and seismology, and their multidimensional analogues are especially important for applied work. However, whereas results have been established for the some narrow classes of hyperbolic equations, no results exist for more general classes. This paper proves the solvability of the inverse problem for a general class of multidimensional hyperbolic equations. Our approach consists of properly choosing the shape of the overidentifying condition that is needed to determine the right-hand side of the hyperbolic PDE and then applying the Fourier series method. We are then able to establish the results of the existence of solution for the cases when the unknown right-hand side is time- independent or space independent.