On a Hyperbolic Coefficient Inverse Problem via Partial Dynamic Boundary Measurements

This paper is devoted to the identification of the unknown smooth coefficient c entering the hyperbolic equation c(x)2 t u-u = 0 in a bounded smooth domain in Rd 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 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. Key words. inverse problem, hyperbolic equation, geometric control, identification

• Type: Journal
• Year: 2010
• Where: JAM
• Authors: Christian Daveau, Diane Manuel Douady, Abdessatar Khelifi
• Keywords: Dynamic Boundary Measurements, Hyperbolic Equation, JAM 2010, Partial Cauchy Data