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Zbl 1200.35321
Daveau, Christian; Douady, Diane Manuel; Khelifi, Abdessatar
On a hyperbolic coefficient inverse problem via partial dynamic boundary measurements.
(English)
[J] J. Appl. Math. 2010, Article ID 561395, 14 p. (2010). ISSN 1110-757X; ISSN 1687-0042/e

Summary: This paper is devoted to the identification of the unknown smooth coefficient $c$ entering the hyperbolic equation $c(x)\partial_t^2u -\Delta u=0$ in a bounded smooth domain in $\Bbb R^d$ 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.
MSC 2000:
*35R30 Inverse problems for PDE
49J20 Optimal control problems with PDE (existence)

Keywords: hyperbolic PDE; inverse problem; geometrical control method; Dirichlet-to-Neumann maps

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