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31
Thermoacoustic tomography with variable sound speed
 Inverse Problems
, 2009
"... Abstract. We study the mathematical model of thermoacoustic tomography in media with a variable speed for a fixed time interval [0, T] so that all signals issued from the domain leave it after time T. In case of measurements on the whole boundary, we give an explicit solution in terms of a Neumann s ..."
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Cited by 42 (12 self)
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Abstract. We study the mathematical model of thermoacoustic tomography in media with a variable speed for a fixed time interval [0, T] so that all signals issued from the domain leave it after time T. In case of measurements on the whole boundary, we give an explicit solution in terms of a Neumann series expansion. We give almost necessary and sufficient conditions for uniqueness and stability when the measurements are taken on a part of the boundary. 1.
An Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control parabolic equations
 ESAIM Control Optim. Calc. Var
"... Abstract. Local and global Carleman estimates play a central role in the study of some partial differential equations regarding questions such as unique continuation and controllability. We survey and prove such estimates in the case of elliptic and parabolic operators by means of semiclassical mi ..."
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Cited by 28 (3 self)
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Abstract. Local and global Carleman estimates play a central role in the study of some partial differential equations regarding questions such as unique continuation and controllability. We survey and prove such estimates in the case of elliptic and parabolic operators by means of semiclassical microlocal techniques. Optimality results for these estimates and some of their consequences are presented. We point out the connexion of these optimality results to the local phasespace geometry after conjugation with the weight function. Firstly, we introduce local Carleman estimates for elliptic operators and deduce unique continuation properties as well as interpolation inequalities. These latter inequalities yield a remarkable spectral inequality and the null controllability of the heat equation. Secondly, we prove Carleman estimates for parabolic operators. We state them locally in space at first, and patch them together to obtain a global estimate. This second approach also yields
Radiation fields, scattering and inverse scattering on asymptotically hyperbolic manifolds
, 2004
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Introduction to spectral theory and inverse problems on asymptotically hyperbolic manifolds, preprint
, 2011
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Conditional stability for illposed elliptic Cauchy problems : the case
 of C 1,1 domains (part I). Rapport INRIA n6585
, 2008
"... apport de recherche ..."
Unique continuation along curves and hypersurfaces for second order anisotropic hyperbolic systems with real analytic coefficients
 Proc. Amer. Math. Soc
"... Abstract. In this paper we prove the following kind of the unique continuation property. That is the zero on each geodesic of the solution in a real analytic hypersurface for second order anisotropic hyperbolic system with real analytic coefficients can be continued along this curve. 1. ..."
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Abstract. In this paper we prove the following kind of the unique continuation property. That is the zero on each geodesic of the solution in a real analytic hypersurface for second order anisotropic hyperbolic system with real analytic coefficients can be continued along this curve. 1.
Unique continuation and an inverse problem for hyperbolic equations across a general hypersurface
, 2004
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Multiwave methods via ultrasound
, 2012
"... Abstract. We present a survey of the recent results by the authors on multiwave methods where the high resolution method is ultrasound. We consider the inverse problem of determining a source inside a medium from ultrasound measurements made on the boundary of the medium. Some multiwave medical im ..."
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Abstract. We present a survey of the recent results by the authors on multiwave methods where the high resolution method is ultrasound. We consider the inverse problem of determining a source inside a medium from ultrasound measurements made on the boundary of the medium. Some multiwave medical imaging methods where this is considered are photoacoustic tomography, thermoacoustic tomography, ultrasound modulated tomography, transient elastography and magnetoacoustic tomography. In case of measurements on the whole boundary, we give an explicit solution in terms of a Neumann series expansion. We give almost necessary and sufficient conditions for uniqueness and stability when the measurements are taken on a part of the boundary. We study the case of a smooth speed and speeds having jump type of singularities. The latter models propagation of acoustic waves in the brain where the skull has a much larger sound speed than the rest of the brain. In this paper we emphasize a microlocal viewpoint. 1.
1 Waves, damped wave and observation ∗
"... This talk describes some applications of two kinds of observation estimate for the wave equation and for the damped wave equation in a bounded domain where the geometric control condition of C. Bardos, G. Lebeau and J. Rauch may failed. 1 The ..."
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This talk describes some applications of two kinds of observation estimate for the wave equation and for the damped wave equation in a bounded domain where the geometric control condition of C. Bardos, G. Lebeau and J. Rauch may failed. 1 The