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- Title
Exponential convergence to steady-states for trajectories of a damped dynamical system modeling adhesive strings.
- Authors
Coclite, Giuseppe Maria; De Nitti, Nicola; Maddalena, Francesco; Orlando, Gianluca; Zuazua, Enrique
- Abstract
We study the global well-posedness and asymptotic behavior for a semilinear damped wave equation with Neumann boundary conditions, modeling 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.
- Subjects
DYNAMICAL systems; NEUMANN boundary conditions; ADHESIVES; WAVE equation; RIGID bodies; SEMILINEAR elliptic equations
- Publication
Mathematical Models & Methods in Applied Sciences, 2024, Vol 34, Issue 8, p1445
- ISSN
0218-2025
- Publication type
Article
- DOI
10.1142/S021820252450026X