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...

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Bibliographic Details
Published in:Journal of dynamics and differential equations 2020-12, Vol.32 (4), p.1997-2020
Main Authors: Ramos, Anderson J. A., Santos, Manoel J. Dos, Freitas, Mirelson M., Almeida Júnior, Dilberto S.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Controllability
Damping
Delay
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
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Summary: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.
ISSN:1040-7294
1572-9222
DOI:10.1007/s10884-019-09799-2