Global uniqueness and stability in determining the damping and potential coefficients of an inverse hyperbolic problem

We consider a second-order hyperbolic equation on an open bounded domain Omega in R-n for n >= 2, with C-2-boundary Gamma = partial derivative Omega = (Gamma(0)boolean OR Gamma(1)) over bar, Gamma(0) boolean AND Gamma(1) = Gamma(1) = empty set, subject to non-homogeneous Neumann boundary conditions on the entire boundary Gamma. We then study the inverse problem of determining both the interior damping and potential coefficients of the equation in one shot by means of an additional measurement of the Dirichlet boundary trace of the solution, in a suitable, explicit sub-portion Gamma(1) of the boundary Gamma, and over a computable time interval T > 0. Under sharp conditions on the complementary part Gamma(0) = Gamma \ Gamma(1), T > 0, and under weak regularity requirements on the data, we establish the two canonical results of the inverse problem: (i) global uniqueness and (ii) stability. The latter (ii) is the main result of the paper. Our proof relies on three main ingredients