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arXiv · 2311.05295

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

Giuseppe Maria Coclite·Nicola De Nitti·Francesco Maddalena·Gianluca Orlando·Enrique Zuazua
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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.

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Giuseppe Maria Coclite, Nicola De Nitti, Francesco Maddalena, Gianluca Orlando, Enrique Zuazua. 2023-11-09. Exponential convergence to steady-states for trajectories of a damped dynamical system modelling adhesive strings. https://arxiv.org/abs/2311.05295

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