Advances in Difference Equations
Volume 2010 (2010), Article ID 748789, 15 pages
Research Article

Exponential Stability and Global Attractors for a Thermoelastic Bresse System

College of Science, Shanghai Second Polytechnic University, Shanghai 201209, China

Received 13 September 2010; Accepted 29 October 2010

Academic Editor: E. Thandapani

Copyright © 2010 Zhiyong Ma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider the stability properties for thermoelastic Bresse system which describes the motion of a linear planar shearable thermoelastic beam. The system consists of three wave equations and two heat equations coupled in certain pattern. The two wave equations about the longitudinal displacement and shear angle displacement are effectively damped by the dissipation from the two heat equations. We use multiplier techniques to prove the exponential stability result when the wave speed of the vertical displacement coincides with the wave speed of the longitudinal or of the shear angle displacement. Moreover, the existence of the global attractor is firstly achieved.