Michael V. Klibanov, Sergey I. Kabanikhin and Dmitrii V. Nechaev
Numerical solution of the problem of the computational time reversal in the quadrant
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ABSTRACT. The problem of the computational time reversal is posed as the inverse problem of the determination of the unknown initial condition with the finite support in the hyperbolic equation, given the Cauchy
data at the lateral surface. A stability estimate for this ill-posed problem implies refocusing of the time reversed wave field. Two such two-dimensional inverse problems are solved numerically in the case
when the domain is a quadrant and the Cauchy data are given at finite parts of the coordinate axis. The previously obtained Lipschitz
stability estimate rigorously explains and numerical results confirm the experimentally observed phenomenon of refocusing of time reversed wave fields.