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An inverse problem of the determination of an initial condition in ahyperbolic equation from the lateral Cauchy data is considered. This problemhas applications to the thermoacoustic tomography, as well as to linearizedcoefficient inverse problems of acoustics and electromagnetics. A new versionof the quasi-reversibility method is described. This version requires a newLipschitz stability estimate, which is obtained via the Carleman estimate.Numerical results are presented.

The Quasi-Reversibility Method for the Thermoacoustic Tomography and a Coefficient Inverse Problem