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.
Publié le : 2007-07-05
Classification:
hyperbolic equation,
Inverse problem,
Carleman inequality,
hyperbolic equation.,
35R30, 35L20,
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
@article{hal-00271925,
author = {Baudouin, Lucie and Mercado, Alberto and Osses, Axel},
title = {A global Carleman estimate in a transmission wave equation and application to a one-measurement inverse problem.},
journal = {HAL},
volume = {2007},
number = {0},
year = {2007},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00271925}
}
Baudouin, Lucie; Mercado, Alberto; Osses, Axel. A global Carleman estimate in a transmission wave equation and application to a one-measurement inverse problem.. HAL, Tome 2007 (2007) no. 0, . http://gdmltest.u-ga.fr/item/hal-00271925/