Calculus of Variations and Geometric Measure Theory

G. M. 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

created by orlando on 10 Jul 2024


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

ArXiv: 2311.05295 PDF


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.