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Stability to weakly dissipative Timoshenko systems

In this paper, we consider the Timoshenko systems with frictional dissipation working only on the vertical displacement. We prove that the system is exponentially stable if and only if the wave speeds are the same. On the contrary, we show that the Timoshenko systems is polynomially stable giving the optimal decay rate. Copyright © 2013 John Wiley & Sons, Ltd.