Lower bound and optimality for a nonlinearly damped Timoshenko system with thermoelasticity

Ahmed Bchatnia, Sabrine Chebbi, Makram Hamouda, Abdelaziz Soufyane

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 Alabau-Boussouira’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).