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

Coclite GM, De Nitti N, Maddalena F, Orlando G, Zuazua Iriondo E (2024)

Publication Language: English

Publication Status: Accepted

Publication Type: Unpublished / Preprint

Future Publication Type: Other publication type

Publication year: 2024

Journal

Mathematical Models & Methods in Applied Sciences World Scientific Publishing

Publisher: M3AS

Open Access Link: https://dcn.nat.fau.eu/wp-content/uploads/CocDNMadOrlZua-231029.pdf

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.

Authors with CRIS profile

Nicola De Nitti
Enrique Zuazua Iriondo Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Additional Organisation(s)

Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

Politecnico di Bari IT Italy (IT) École Polytechnique Fédérale de Lausanne (EPFL) CH Switzerland (CH)

How to cite

APA:

Coclite, G.M., De Nitti, N., Maddalena, F., Orlando, G., & Zuazua Iriondo, E. (2024). Exponential convergence to steady-states for trajectories of a damped dynamical system modelling adhesive strings. (Unpublished, Accepted).

MLA:

Coclite, Giuseppe Maria, et al. Exponential convergence to steady-states for trajectories of a damped dynamical system modelling adhesive strings. Unpublished, Accepted. 2024.

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