# American Institute of Mathematical Sciences

doi: 10.3934/dcdss.2021086
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## New stability result for a Bresse system with one infinite memory in the shear angle equation

 1 The Preparatory Year Program 2 The Interdisciplinary Research Center in Construction and Building Materials, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia 3 Department of Basic Engineering Sciences, College of Engineering, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam 34151, Saudi Arabia

* Corresponding author: Adel M. Al-Mahdi

Received  March 2021 Revised  May 2021 Early access July 2021

Fund Project: This paper is supported by KFUPM grant #SB191037

In this paper, we consider a one-dimensional linear Bresse system with only one infinite memory acting in the second equation (the shear angle equation) of the system. We prove that the asymptotic stability of the system holds under some general condition imposed into the relaxation function, precisely,
 $g^{\prime}(t)\le -\xi(t) G(g(t)).$
The proof is based on the multiplier method and makes use of convex functions and some inequalities. More specifically, we remove the constraint imposed on the boundedness condition on the initial data
 $\eta{0x}$
. This study generalizes and improves previous literature outcomes.
Citation: Adel M. Al-Mahdi, Mohammad M. Al-Gharabli, Saeed M. Ali. New stability result for a Bresse system with one infinite memory in the shear angle equation. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2021086
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