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Decay rate of the Timoshenko system with one boundary damping

Abstract : In this paper, we study the indirect boundary stabilization of the Timoshenko system with only one dissipation law. This system, which models the dynamics of a beam, is a hyperbolic system with two wave speeds. Assuming that the wave speeds are equal, we prove exponential stability. Otherwise, we show that the decay rate is of exponential or polynomial type. Note that the results hold without the technical assumptions on the coefficients coming from the multiplier method: a sharp analysis of the behaviour of the resolvent operator along the imaginary axis is performed to avoid those artificial restrictions.
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Submitted on : Tuesday, September 28, 2021 - 9:06:24 AM
Last modification on : Tuesday, October 19, 2021 - 11:38:59 AM

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Denis Mercier, Virginie Régnier. Decay rate of the Timoshenko system with one boundary damping. Evolution Equations and Control Theory, American Institute of Mathematical Sciences (AIMS), 2019, 8 (2), pp.423-445. ⟨10.3934/eect.2019021⟩. ⟨hal-03142506⟩

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