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

TL;DR

This paper addresses inverse problems for second order hyperbolic equations with time-dependent coefficients, demonstrating the unique determination of the Lorentzian metric from boundary data using an adapted Boundary Control method.

Contribution

It introduces a novel application of the Boundary Control method to determine time-dependent Lorentzian metrics from boundary measurements in hyperbolic equations.

Findings

Unique determination of the Lorentzian metric from boundary data

Extension of Boundary Control method to time-dependent coefficients

Applicability to general second order hyperbolic equations

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].