On a semilinear Timoshenko-Coleman-Gurtin system: Quasi-stability and attractors

Baowei Feng

doi:10.3934/dcds.2017203

Article Contents

2017, Volume 37, Issue 9: 4729-4751. Doi: 10.3934/dcds.2017203

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On a semilinear Timoshenko-Coleman-Gurtin system: Quasi-stability and attractors

Baowei Feng

Department of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China

Received: November 30, 2016

Revised: March 31, 2017

Published: October 2017

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Abstract

A semilinear Timoshenko-Coleman-Gurtin system is studied. The system describes a Timoshenko beam coupled with a temperature with Coleman-Gurtin law. Under some assumptions on nonlinear damping terms and nonlinear source terms, we establish the global well-posedness of the system. The main result is the long-time dynamics of the system. By using the methods developed by Chueshov and Lasiecka, we get the quasi-stability property of the system and obtain the existence of a global attractor which has finite fractal dimension. Result on exponential attractors of the system is also proved.

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

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