Quasi-stability property and attractors  for a semilinear Timoshenko system

Luci H.  Fatori; Marcio A. Jorge  Silva; Vando Narciso

doi:10.3934/dcds.2016067

Article Contents

2016, Volume 36, Issue 11: 6117-6132. Doi: 10.3934/dcds.2016067

This issue Previous Article The Camassa-Holm equation as the long-wave limit of the improved Boussinesq equation and of a class of nonlocal wave equations Next Article Positive and nodal solutions for parametric nonlinear Robin problems with indefinite potential

Quasi-stability property and attractors for a semilinear Timoshenko system

1.
Department of Mathematics, State University of Londrina, Londrina PR, 86057-970
2.
Center of exact sciences, State University of Mato Grosso do Sul, Dourados, 79804-970

Received: December 2015

Revised: February 2016

Published: May 2017

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Abstract

This paper is concerned with the classical Timoshenko system for vibrations of thin rods. It has been studied by many authors and most of known results are concerned with decay rates of the energy, controllability and numerical approximations. There are just a few references on the long-time dynamics of such systems. Motivated by this scenario we establish the existence of global and exponential attractors for a class of semilinear Timoshenko systems with linear frictional damping acting on the whole system and without assuming the well-known equal wave speeds condition.

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Mathematics Subject Classification: Primary: 35B40, 35B41, 35L53; Secondary: 74K10, 93D20.

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