Stabilisation frontière indirecte du système de Timoshenko

Fine scales of decay of operator semigroups

“…The result above has already found a number of applications to the study of concrete PDEs, see e.g. [1], [2], [3], [8], [26], [29], [30], [32], [33], [34], [37], [58], [59], [63], [66]. In view of its importance, Theorem 1.2 (and Theorem 1.1) raised the natural and important problem of obtaining similar results for growth scales which are finer than polynomial ones, or showing that for other scales results of this kind cannot be true.…”

Stability to weakly dissipative Timoshenko systems

“…Recently, Bassam et al . considered an indirect boundary stabilization of the Timoshenko systems with only one dissipation; and under the equal speed wave propagation condition, they established the exponential stability of the system. Otherwise, they showed the polynomial decay.…”

“…Muñoz Rivera and Racke [6] studied a linear case with dissipation a t .a > 0/, and Alabau-Boussouira [7] considered a nonlinear feedback force acting only in the equation for the rotational angle. Recently, Bassam et al [8] considered an indirect boundary stabilization of the Timoshenko systems with only one dissipation; and under the equal speed wave propagation condition, they established the exponential stability of the system. Otherwise, they showed the polynomial decay.…”

A localized nonstandard stabilizer for the Timoshenko beam

“…In particular, it is known that when a single dissipation acting through the shear angle equation is utilized, the associated semigroup is exponentially stable if and only if the speeds of propagation of the corresponding waves are equal, e.g. [1,2,4,7,13,15,16,18]:…”