A global Carleman estimate in a transmission wave equation and application to a one-measurement inverse problem

Details A global Carleman estimate in a transmission wave equation and application to a one-measurement inverse problem A global Carleman estimate in a transmission wave equation and application to a one-measurement inverse problem

2008-04-10

arxiv.org/abs/0804.1709v1

Inverse Problems 23, 1 (2007) 257-278

Mathematics

Analysis of PDEs

Scientific paper

10.1088/0266-5611/23/1/014

We consider a transmission wave equation in two embedded domains in $R^2$, where the speed is $a1 > 0$ in the inner domain and $a2 > 0$ in the outer domain. We prove a global Carleman inequality for this problem under the hypothesis that the inner domain is strictly convex and $a1 > a2$ . As a consequence of this inequality, uniqueness and Lip- schitz stability are obtained for the inverse problem of retrieving a stationary potential for the wave equation with Dirichlet data and discontinuous principal coefficient from a single time-dependent Neumann boundary measurement.

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