Asymptotic behavior for Timoshenko beams subject to a single nonlinear feedback control

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INDIRECT STABILIZATION OF LOCALLY COUPLED WAVE-TYPE SYSTEMS (2012, background): “One can show that polynomial stability holds through indirect mechanisms (see [8], [10] and the references therein) such as the ones considered in the present paper.”
Sharp energy estimates for nonlinearly locally damped PDEs via observability for the associated undamped system (2011, methodology): “We show by this way that for the locally distributed case, one can combine the optimal geometric optics conditions of Bardos, Lebeau and Rauch [10] (see also [11,12]) and the optimalweight convexity method by the first author [1,2,6] (see also [3,4]) based on nonlinear Gronwall inequalities with opt”
Stability to weakly dissipative Timoshenko systems (2013, background): “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.”