Abstract
In this paper, we consider a vibrating nonlinear Timoshenko system with thermoelasticity with second sound. We first investigate the stability of this system, then we devote our efforts to obtain the strong lower energy estimates using AlabauBoussouira's energy comparison principle introduced in (J. Differ Equations 248 (2010), 1473-1517) (see also NoDEA Nonlinear Differential Equations Appl. 18(5) (2011), 571-597). We extend to our model the results achieved in (NoDEA Nonlinear Differential Equations Appl. 18(5) (2011), 571-597) for the case of nonlinearly damped Timoshenko system with thermoelasticity. The proof of our results relies on the approach in (NoDEA Nonlinear Differential Equations Appl. 14(5-6) (2007), 643-669 and Appl. Math. Optim. 51(1) (2005), 61-105).