# American Institute of Mathematical Sciences

November  2003, 9(6): 1625-1639. doi: 10.3934/dcds.2003.9.1625

## Global stability for damped Timoshenko systems

 1 Department of Research and Development, National Laboratory for Scientific Computation, Rua Getulio Vargas 333, Quitandinha, CEP 25651-070, Petrópolis, RJ and UFRJ, Rio de Janeiro, Brazil 2 Department of Mathematics and Statistics, University of Konstanz, 78457 Konstanz, Germany

Received  July 2002 Revised  September 2003 Published  September 2003

We consider a nonlinear Timoshenko system as an initial-boundary value problem in a one-dimensional bounded domain. The system has a dissipative mechanism through frictional damping being present only in the equation for the rotation angle. We first give an alternative proof for a sufficient and necessary condition for exponential stability for the linear case. Polynomial stability is proved in general. The global existence of small, smooth solutions and the exponential stability is investigated for the nonlinear case.
Citation: J.E. Muñoz Rivera, Reinhard Racke. Global stability for damped Timoshenko systems. Discrete & Continuous Dynamical Systems - A, 2003, 9 (6) : 1625-1639. doi: 10.3934/dcds.2003.9.1625
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