Exponential convergence to steady-states for trajectories of a damped dynamical system modelling adhesive strings
Analysis of PDEs
2023-11-10 v1
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.
Keywords
Cite
@article{arxiv.2311.05295,
title = {Exponential convergence to steady-states for trajectories of a damped dynamical system modelling adhesive strings},
author = {Giuseppe Maria Coclite and Nicola De Nitti and Francesco Maddalena and Gianluca Orlando and Enrique Zuazua},
journal= {arXiv preprint arXiv:2311.05295},
year = {2023}
}