Global stability for damped Timoshenko systems

Pages: 1625 - 1639, Volume 9, Issue 6, November 2003

doi:10.3934/dcds.2003.9.1625       Abstract        Full Text (167.1K)       Related Articles

J.E. Muñoz Rivera - 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 (email)
Reinhard Racke - Department of Mathematics and Statistics, University of Konstanz, 78457 Konstanz, Germany (email)

Abstract: 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.

Keywords:  Nonlinear Timoshenko beam, frictional damping, exponential stability.
Mathematics Subject Classification:  35B40.

Received: July 2002;      Revised: September 2003;      Published: September 2003.