Journal of Applied Mathematics
Volume 2010 (2010), Article ID 561395, 14 pages
Research Article

On a Hyperbolic Coefficient Inverse Problem via Partial Dynamic Boundary Measurements

1Département de Mathématiques, CNRS AGM UMR 8088, Université de Cergy-Pontoise, 95302 Cergy-Pontoise Cedex, France
2Département de Mathématiques, Université des Sciences de Carthage, 7021 Bizerte, Tunisia

Received 29 March 2010; Revised 31 May 2010; Accepted 1 June 2010

Academic Editor: Christo I. Christov

Copyright © 2010 Christian Daveau et al. 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.


This paper is devoted to the identification of the unknown smooth coefficient c entering the hyperbolic equation c(x)t2uΔu=0 in a bounded smooth domain in d from partial (on part of the boundary) dynamic boundary measurements. In this paper, we prove that the knowledge of the partial Cauchy data for this class of hyperbolic PDE on any open subset Γ of the boundary determines explicitly the coefficient c provided that c is known outside a bounded domain. Then, through construction of appropriate test functions by a geometrical control method, we derive a formula for calculating the coefficient c from the knowledge of the difference between the local Dirichlet-to-Neumann maps.