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A new version of the quasi-reversibility method for the thermoacoustic tomography and a coefficient inverse problem

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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.
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Keywords: Carleman estimate; imaging of sharp peaks; numerical results; quasi-reversibility method

Document Type: Research Article

Affiliations: 1: Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, USA 2: Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Science-Prospect Acad., Novosibirsk, Russia 3: Lavrent'ev Institute of Hydrodynamics of the Siberian Branch of the Russian Academy of Science-Prospect Acad., Novosibirsk, Russia

Publication date: 2008-10-01

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