Abstract
An inverse problem of the determination of an initial condition in a hyperbolic equation from the lateral Cauchy data is considered. This problem has applications to the thermoacoustic tomography, as well as to linearized coefficient inverse problems of acoustics and electromagnetics. A new version of the quasi-reversibility method is described. This version requires a new Lipschitz stability estimate, which is obtained via the Carleman estimate. Numerical results are presented.
Acknowledgements
The research of M.V. Klibanov and A.V. Kuzhuget was supported by the U.S. Army Research Laboratory and U.S. Army Research Office under contract/grant number W911NF-05-1-0378. M.V. Klibanov has performed a part of this work during the Special Semester on Quantative Biology Analyzed by Mathematical Methods, 1 October 2007 to 27 January 2008, organized by RICAM, Austrian Academy of Sciences.