Published Paper

Inserted: 10 jul 2024
Last Updated: 10 jul 2024

Journal: Math. Models Methods Appl. Sci.
Volume: 34
Number: 08
Pages: 1445-1482
Year: 2023
Doi: 10.1142/S021820252450026X

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.