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Lipschitz stability in an inverse problem for a hyperbolic equation with a finite set of boundary data

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Abstract:

We consider an inverse problem of determining multiple coefficients of principal part of a scalar hyperbolic equation with Dirichlet boundary data. We prove the uniqueness and a Lipschitz stability estimate in the inverse problem with some observations on a suitable sub-boundary satisfying an appropriate geometrical condition. The key is a Carleman estimate for a hyperbolic operator with variable coefficients.

Keywords: Lipschitz stability; anisotropic media; inverse hyperbolic problems

Document Type: Research Article

DOI: https://doi.org/10.1080/00036810802369231

Affiliations: 1: Faculte des Sciences de Bizerte, Department des Mathematiques, University of Carthage, Tunisia 2: Department of Mathematical Sciences, The University of Tokyo, Tokyo, Japan

Publication date: 2008-10-01

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