GM. Coclite, N. De Nitti, F. Maddalena, G. Orlando, E. Zuazua. Exponential convergence to steady-states for trajectories of a damped dynamical system modelling adhesive strings (2024) M3AS
Abstract. 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.