  We study the global well-posedness and asymptotic behavior for a semilinear
damped wave equation with Neumann boundary conditions, modelling a
one-dimensional linearly elastic body interacting with a rigid substrate
through an adhesive material. The key feature of of the problem is that the
interplay between the nonlinear force and the boundary conditions allows for a
continuous set of equilibrium points. We prove an exponential rate of
convergence for the solution towards a (uniquely determined) equilibrium point.
