Affiliations: [a] UR Analyse Non-Linéaire et Géometrie, UR13ES32, Department of Mathematics, Faculty of Sciences of Tunis, University of Tunis El-Manar, 2092 El Manar II, Tunisia. E-mails: ahmed.bchatnia@fst.utm.tn, sabrine.chebbi@fst.utm.tn | [b] Institute for Scientific Computing and Applied Mathematics, Indiana University, 831 E. 3rd St., Rawles Hall, Bloomington IN 47405, United States. E-mail: mahamoud@indiana.edu | [c] Department of Mathematics, College of Sciences, University of Sharjah, P.O.Box 27272, Sharjah, UAE. E-mail: asoufyane@sharjah.ac.ae
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).
