Global stability for damped Timoshenko systems

J.E. Muñoz Rivera; Reinhard Racke

doi:10.3934/dcds.2003.9.1625

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2003, Volume 9, Issue 6: 1625-1639. Doi: 10.3934/dcds.2003.9.1625

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Global stability for damped Timoshenko systems

J.E. Muñoz Rivera^1, and
Reinhard Racke^2,

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
2.
Department of Mathematics and Statistics, University of Konstanz, 78457 Konstanz

Received: June 30, 2002

Revised: August 31, 2003

Published: October 2003

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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.

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Mathematics Subject Classification: 35B40.

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