Open Access
2010 On a Hyperbolic Coefficient Inverse Problem via Partial Dynamic Boundary Measurements
Christian Daveau, Diane Manuel Douady, Abdessatar Khelifi
J. Appl. Math. 2010: 1-14 (2010). DOI: 10.1155/2010/561395


This paper is devoted to the identification of the unknown smooth coefficient c entering the hyperbolic equation $c\left(x\right){\partial }_{t}^{2}u-\Delta u=0$ in a bounded smooth domain in ${ℝ}^{d}$ 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 $\Gamma $ 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.


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Christian Daveau. Diane Manuel Douady. Abdessatar Khelifi. "On a Hyperbolic Coefficient Inverse Problem via Partial Dynamic Boundary Measurements." J. Appl. Math. 2010 1 - 14, 2010.


Published: 2010
First available in Project Euclid: 1 November 2010

zbMATH: 1200.35321
MathSciNet: MR2726984
Digital Object Identifier: 10.1155/2010/561395

Rights: Copyright © 2010 Hindawi

Vol.2010 • 2010
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