Invariance of decay rate with respect to boundary conditions in thermoelastic Timoshenko systems

This paper is mainly concerned with the polynomial stability of a thermoelastic Timoshenko system recently introduced by Almeida Junior 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.