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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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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.
Radiation fields, scattering and inverse scattering on asymptotically hyperbolic manifolds
, 2004
"... ..."
Conditional stability for illposed elliptic Cauchy problems : the case
 of C 1,1 domains (part I). Rapport INRIA n6585
, 2008
"... apport de recherche ..."
Identification of
"... : We consider the problem of recovering the coefficient q(x) in the equation u t = \Delta\Delta \Deltau \Gamma qu from boundary observations. Uniqueness of q based on knowledge of the `Neumann 7! Dirichlet response operator' is shown as an implication of (known) corresponding results concerning th ..."
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: We consider the problem of recovering the coefficient q(x) in the equation u t = \Delta\Delta \Deltau \Gamma qu from boundary observations. Uniqueness of q based on knowledge of the `Neumann 7! Dirichlet response operator' is shown as an implication of (known) corresponding results concerning the inverse problem for the corresponding hyperbolic equation w tt = \Delta\Delta \Delta w \Gamma qw. This is then reduced to use of the response to a single input with some consideration of computational approximation. Key Words: identification, parabolic, partial differential equation, uniqueness, approximation. 1 This research has been partially supported by the U.S. National Academy of Science under the NAS/NRC Project Development Program. 1. Introduction We consider the problem of identifying the (unknown) coefficient q = q(x) in the parabolic partial differential equation u t = \Delta\Delta \Deltau \Gamma qu on Q := (0; T ) \Theta\Omega ; (1.1) assuming input/output access only a...
HYPERBOLIC EQUATION WITH VARIABLE COEFFICIENTS
, 2004
"... Stability estimate in a Cauchy problem for a hyperbolic equation with variable coefficients by ..."
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Stability estimate in a Cauchy problem for a hyperbolic equation with variable coefficients by
KOMABA, TOKYO, JAPANTHE CONDITIONAL STABILITY IN LINE UNIQUE CONTINUATION FOR A WAVE EQUATION AND AN INVERSE WAVE SOURCE PROBLEM
, 2005
"... The conditional stability in line unique continuation for a wave equation and an inverse wave source problem by ..."
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The conditional stability in line unique continuation for a wave equation and an inverse wave source problem by
KOMABA, TOKYO, JAPANUNIQUE CONTINUATION AND AN INVERSE PROBLEM FOR HYPERBOLIC EQUATIONS ACROSS A GENERAL HYPERSURFACE
, 2004
"... Unique continuation and an inverse problem for hyperbolic equations across a general hypersurface by ..."
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Unique continuation and an inverse problem for hyperbolic equations across a general hypersurface by
RAPPORTEURS:
, 2013
"... Uniform controllability of discrete partial di erential equations THÈSE dirigée par: ..."
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Uniform controllability of discrete partial di erential equations THÈSE dirigée par: