On the decay rates of Timoshenko system with second sound |
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| Authors: | Tijani A Apalara Salim A Messaoudi Ahmed A Keddi |
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| Institution: | 1. Mathematics Department, University of Hafr Al‐Batin, Hafr Al‐Batin 31991, Saudi Arabia;2. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia;3. Department of Mathematics, Djillali Liabes University, Algeria |
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| Abstract: | In this work, we study the well‐posedness and the asymptotic stability of a one‐dimensional linear thermoelastic Timoshenko system, where the heat conduction is given by Cattaneo's law and the coupling is via the displacement equation. We prove that the system is exponentially stable provided that the stability number χτ=0. Otherwise, we show that the system lacks exponential stability. Furthermore, in the latter case, we show that the solution decays polynomially. Copyright © 2015 John Wiley & Sons, Ltd. |
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| Keywords: | well‐posedness exponential stability polynomial stability thermoelasticity Timoshenko second sound Cattaneo's law |
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