Title: Stability for thermo-elastic Bresse system of second sound with past history and delay term

Authors: Khaled Zennir; Djamel Ouchenane; Abdelbaki Choucha

Addresses: Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass, Saudi Arabia ' Laboratory of Pure and Applied Mathematics, Amar Teledji Laghouat University, BP G37 (M'kam) 03000, Algeria ' Faculty of Exact Sciences, Department of Mathematics, University of El Oued, B.P. 789, El Oued 39000, Algeria

Abstract: In the present paper, one-dimensional linear thermo-elastic system of Bresse type with past history and delay term is considered. We prove the well-posedness of problem using the semigroup method. By using the energy method, we discuss stability of the system for two cases. An exponential stability result of system (7) is obtained in the case where the propagation velocities are equal in equation of vertical displacement and the equation of system rotation angle in equation (59). Furthermore, a result of algebraic stability is obtained in the case of the different propagation velocities in equation (60), where the initial data E₂(0) is involved in the decay rate. We extend results in Zitouni et al. (2018) by using techniques of Zennir and Feng (2018).

Keywords: Bresse system; thermo-elastic; past history; delay; asymptotic stability; energy method; semigroup method.

DOI: 10.1504/IJMIC.2020.117488

International Journal of Modelling, Identification and Control, 2020 Vol.36 No.4, pp.315 - 328

Received: 25 Jun 2020
Accepted: 20 Oct 2020
Published online: 09 Sep 2021 *

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