Stability for thermo-elastic Bresse system of second sound with past history and delay term
by Khaled Zennir; Djamel Ouchenane; Abdelbaki Choucha
International Journal of Modelling, Identification and Control (IJMIC), Vol. 36, No. 4, 2020

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).

Online publication date: Thu, 09-Sep-2021

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