Lower Bound and optimality for a nonlinearly damped Timoshenko system\n with thermoelasticity

2017/03/07 by Ahmed Bchatnia, Sabrine Chebbi, Bchatnia, Ahmed +5
Computer Science · Engineering · Mathematics · #35B35 #35B40 #35L51 #93D20 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1703.02599

openalex publication_date 2017/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider a vibrating nonlinear Timoshenko system with\nthermoelasticity with second sound. We first investigate the strong stability\nof this system, then we devote our efforts to obtain the strong lower energy\nestimates using Alabau--Boussouira's energy comparison principle introduced in\n cite2 (see also citealabau). One of the main advantages of these results\nis that they allows us to prove the optimality of the asymptotic results (as\nt\→ \∞) obtained in citeali. We also extend to our model the\nnice results achieved in citealabau for the case of nonlinearly damped\nTimoshenko system with thermoelasticity. The optimality of our results is also\ninvestigated through some explicit examples of the nonlinear damping term. The\nproof of our results relies on the approach in citeAB1, AB2.\n

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