DETERMINING DAMPING AND POTENTIAL COEFFICIENTS OF AN INVERSE PROBLEM FOR A SYSTEM OF TWO COUPLED HYPERBOLIC EQUATIONS. PART I: GLOBAL UNIQUENESS

We study a uniqueness inverse problem for two coupled hyperbolic PDEs with Neumann boundary conditions by means of an additional measurement of Dirichlet boundary Gamma traces of the two solutions on a suitable, explicit sub-portion Gamma(1) of the boundary, and over a computable time interval T > 0. Under sharp conditions on Gamma(0) = Gamma\Gamma(1), T > 0, we establish uniqueness of both the damping and potential coefficients for each equation. The proof uses critically the Carleman estimate in [11], together with a suggestion in [8, Thm 8.2.2, p. 231]. A Riemannian version would also hold, this time by using the corresponding Carleman estimates in [19].