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.

Exponential convergence to steady-states for trajectories of a damped dynamical system modeling adhesive strings / Coclite, Giuseppe Maria; De Nitti, Nicola; Maddalena, Francesco; Orlando, Gianluca; Zuazua, Enrique. - In: MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. - ISSN 0218-2025. - STAMPA. - 34:08(2024), pp. 1445-1482. [10.1142/s021820252450026x]

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

Coclite, Giuseppe Maria;Maddalena, Francesco;Orlando, Gianluca;Zuazua, Enrique
2024-01-01

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.
2024
Exponential convergence to steady-states for trajectories of a damped dynamical system modeling adhesive strings / Coclite, Giuseppe Maria; De Nitti, Nicola; Maddalena, Francesco; Orlando, Gianluca; Zuazua, Enrique. - In: MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. - ISSN 0218-2025. - STAMPA. - 34:08(2024), pp. 1445-1482. [10.1142/s021820252450026x]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/270040
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