Inverse problems for general second order hyperbolic equations with time-dependent coefficients

Abstract

We study the inverse problems for the second order hyperbolic equations of general form with time-dependent coefficients assuming that the boundary data are given on a part of the boundary. The main result of this paper is the determination of the time-dependent Lorentzian metric by the boundary measurements. This is achieved by the adaptation of a variant of the Boundary Control method developed by the author in [E1], [E2].

Corrections suggested by the referee are made, Bull. Math. Sci. (2017)

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