Abstract
This paper is mainly concerned with the polynomial stability of a thermoelastic Timoshenko system recently introduced by Almeida Júnior et al. (Z Angew Math Phys 65(6):1233–1249, 2014) that proved, in the general case when equal wave speeds are not assumed, different polynomial decay rates depending on the boundary conditions, namely, optimal rate \({t^{-1/2}}\) for mixed Dirichlet–Neumann boundary condition and rate \({t^{-1/4}}\) for full Dirichlet boundary condition. Here, our main achievement is to prove the same polynomial decay rate \({t^{-1/2}}\) (corresponding to the optimal one) independently of the boundary conditions, which improves the existing literature on the subject. As a complementary result, we also prove that the system is exponentially stable under equal wave speeds assumption. The technique employed here can probably be applied to other kind of thermoelastic systems.
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Alves, M.S., Jorge Silva, M.A., Ma, T.F. et al. Invariance of decay rate with respect to boundary conditions in thermoelastic Timoshenko systems. Z. Angew. Math. Phys. 67, 70 (2016). https://doi.org/10.1007/s00033-016-0662-y
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DOI: https://doi.org/10.1007/s00033-016-0662-y