Michael V. Klibanov
On an inverse hyperbolic problem
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ABSTRACT. We consider the inverse problem of recovery of an initial condition of a hyperbolic PDE. This problem is also called sometimes "thermoacoustic tomography". In the past publications both stability estimates and convergent numerical methods for this problem were obtained only under some restrictive conditions imposed on the principal part of the elliptic operator. In this paper logarithmic stability estimates are obatined for an arbitrary variable principal part of that operator. Convergence of the Quasi-Reversibility Method to the exact solution is also established for this case. Both complete and incomplete data collection cases are considered.