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We study the global well-posedness and asymptotic behavior for a semilineardamped wave equation with Neumann boundary conditions, modelling aone-dimensional linearly elastic body interacting with a rigid substratethrough an adhesive material. The key feature of of the problem is that theinterplay between the nonlinear force and the boundary conditions allows for acontinuous set of equilibrium points. We prove an exponential rate ofconvergence for the solution towards a (uniquely determined) equilibrium point.

Exponential convergence to steady-states for trajectories of a damped dynamical system modelling adhesive strings