We are concerned with the inverse problem of determining both the potential
and the damping coefficient in a dissipative wave equation from boundary
measurements. We establish stability estimates of logarithmic type when the
measurements are given by the operator who maps the initial condition to
Neumann boundary trace of the solution of the corresponding initial-boundary
value problem. We build a method combining an observability inequality together
with a spectral decomposition. We also apply this method to a clamped
Euler-Bernoulli beam equation. Finally, we indicate how the present approach
can be adapted to a heat equation