A General Stability for a Modified Type III Thermoelastic Bresse System via the Longitudinal Displacement

Fayssal Djellali, Zayd Hajjej, Hongwei Zhang and Said Mesloub ()
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Fayssal Djellali: Laboratory of Mathematics, Dynamics and Modelization, Badji Mokhtar-Annaba University, P.O. Box 12, Annaba 23000, Algeria
Zayd Hajjej: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Hongwei Zhang: Department of Mathematics, Henan University of Technology, Zhengzhou 450001, China
Said Mesloub: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Mathematics, 2025, vol. 13, issue 21, 1-17

Abstract: This paper studies a one-dimensional thermoelastic Bresse beam model, in which thermal effects governed by the Green–Naghdi theory of heat conduction are coupled specifically with the longitudinal displacement. Assuming appropriate conditions on the memory kernel and by defining a key stability parameter, we prove a unified decay estimate for the system’s energy. This general result includes both exponential and polynomial decay rates as special instances, offering a comprehensive framework for characterizing the system’s long-term behavior.

Keywords: Bresse system; thermoelasticity of type III; general decay; Lyapunov functional (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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