Exponential stability of thermoelastic Timoshenko system with Cattaneo’s law

Exponential stability of Timoshenko-Gurtin-Pipkin systems with full thermal coupling

“…Finally, we mention that the analysis carried out in this work can be adapted also to different boundary conditions. For instance, one can assume the mixed Neumann-Dirichlet boundary conditions considered in [15] ϕ x (0, t) = ϕ x (L, t) = ψ(0, t) = ψ(L, t) = θ(0, t) = θ(L, t) = ξ(0, t) = ξ(L, t) = 0, or any of the boundary conditions considered in [2]. Clearly, appropriate modifications and precise computations must be done, but no substantial challenges arise.…”

“…Note that the system above reduces to (1.6) in the limit situation when τ = ς = 0. The stability properties of the resulting Timoshenko-Cattaneo model with full thermal coupling have been recently analyzed in [15], where it is proved that the associated solution semigroup is exponentially stable independently of the values of the structural parameters. As in the Fourier case, this happens because the system is fully damped, and indeed when the effects of either θ or else ξ are neglected exponential stability holds only within appropriate conditions that somehow generalize the equal wave speed assumption (see [26]).…”

Polynomial stability of thermoelastic Timoshenko system with fractional derivative boundary control

“…The Timoshenko theory originated in 1921 ( [21]), and since then, many authors have studied the stability of Timoshenko systems with Dirichlet, Newmann or mixed boundary ( [8,11,13]). In particular, the effect of wave velocity on the corresponding Timoshenko system is considered in [4,18] and so on.…”