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On a Hyperbolic Coefficient Inverse Problem via Partial Dynamic Boundary Measurements

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  • Christian Daveau
  • Diane Manuel Douady
  • Abdessatar Khelifi

Abstract

This paper is devoted to the identification of the unknown smooth coefficient c entering the hyperbolic equation in a bounded smooth domain in 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 of the boundary determines explicitly the coefficient provided that 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 from the knowledge of the difference between the local Dirichlet-to-Neumann maps.

Suggested Citation

  • Christian Daveau & Diane Manuel Douady & Abdessatar Khelifi, 2010. "On a Hyperbolic Coefficient Inverse Problem via Partial Dynamic Boundary Measurements," Journal of Applied Mathematics, Hindawi, vol. 2010, pages 1-14, September.
    • Handle: RePEc:hin:jnljam:561395
    DOI: 10.1155/2010/561395
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