Global uniqueness and stability in determining the damping coefficient of an inverse hyperbolic problem with non-homogeneous Dirichlet BC through an additional localized Neumann boundary trace

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) = empty set, subject to non-homogeneous Dirichlet boundary conditions on the entire boundary Gamma. We then study the inverse problem of determining the interior damping coefficient of the equation by means of an additional measurement of the Neumann 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 sharp regularity requirements on the data, we establish the two canonical results in inverse problems: (i) uniqueness and Lipschitz stability (at the H-theta-level, 0 < theta <= 1, theta not equal 1/2). The latter (ii) is the main result of this article. Our proof relies on t