GLOBAL UNIQUENESS AND STABILITY IN DETERMINING THE DAMPING COEFFICIENT OF AN INVERSE HYPERBOLIC PROBLEM WITH NONHOMOGENEOUS NEUMANN BC THROUGH AN ADDITIONAL DIRICHLET 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, Gamma(0) boolean AND Gamma(1) = empty set, subject to nonhomogeneous Neumann 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 Dirichlet boundary trace of the solution, in a suitable, explicit subportion Gamma(1) of the boundary G, and over a computable time interval T > 0. Under sharp conditions on the complementary part Gamma(0) = Gamma\Gamma(1), and T > 0, and under weak regularity requirements on the data, we establish the two canonical results in inverse problems: (i) global uniqueness and (ii) Lipschitz stability (at the L(2)-level). The latter is the main result of this paper. Our proof relies on three main ingredients: (a) sharp Carleman estimates at