Inverse Hyperbolic Problems with Time-Dependent Coefficients

Abstract

We consider the inverse problem for the second order hyperbolic equation in a bounded domain in R n with lower order terms depending analytically on the time variable. We prove that the time-dependent Dirichlet-to-Neumann operator prescribed on a part of the boundary uniquely determines the coefficients of the hyperbolic equation up to a diffeomorphism and a gauge transformation. 1 Introduction. Let Ω ⊂ Rn be a bounded domain with a smooth boundary ∂Ω and let Γ0 be an open subset of ∂Ω. Consider a hyperbolic equation in Ω × (0, T0) of the form: