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Existence of Attractors for a Nonlinear Timoshenko System with Delay

Existence of Attractors for a Nonlinear Timoshenko System with Delay This paper deals with Timoshenko’s classic model for beams vibrations. Regarding the linear model of Timoshenko, there are several known results on exponential decay, controllability and numerical approximation, but there are few results that deal with the nonlinear case or even the linear case with delay type damping. In this paper, we will establish the existence of global and exponential attractors for a semilinear Timoshenko system with delay in the rotation angle equation and a friction-type damping in the transverse displacement equation. Since the damping acts on the two equations of the system, we should not assume the well-known velocity equality. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Dynamics and Differential Equations Springer Journals

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References (45)

Publisher
Springer Journals
Copyright
Copyright © Springer Science+Business Media, LLC, part of Springer Nature 2019
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Applications of Mathematics
ISSN
1040-7294
eISSN
1572-9222
DOI
10.1007/s10884-019-09799-2
Publisher site
See Article on Publisher Site

Abstract

This paper deals with Timoshenko’s classic model for beams vibrations. Regarding the linear model of Timoshenko, there are several known results on exponential decay, controllability and numerical approximation, but there are few results that deal with the nonlinear case or even the linear case with delay type damping. In this paper, we will establish the existence of global and exponential attractors for a semilinear Timoshenko system with delay in the rotation angle equation and a friction-type damping in the transverse displacement equation. Since the damping acts on the two equations of the system, we should not assume the well-known velocity equality.

Journal

Journal of Dynamics and Differential EquationsSpringer Journals

Published: Dec 4, 2020

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