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On the decay rates of Timoshenko system with second sound
Author(s) -
Apalara Tijani A.,
Messaoudi Salim A.,
Keddi Ahmed A.
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3720
Subject(s) - exponential stability , thermoelastic damping , mathematics , second sound , work (physics) , exponential decay , mathematical analysis , stability (learning theory) , displacement (psychology) , exponential growth , thermal conduction , coupling (piping) , heat equation , sound (geography) , nonlinear system , physics , thermodynamics , quantum mechanics , thermal , acoustics , mechanical engineering , psychology , machine learning , computer science , engineering , psychotherapist
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 χ τ =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.