Theoretical and computational decay results for a Bresse system with one infinite memory in the longitudinal displacement-Reference-Cited by-同舟云学术

Theoretical and computational decay results for a Bresse system with one infinite memory in the longitudinal displacement

Published:2023 Issue:1 Volume:12 Page:191
ISSN:2163-2480
Container-title:Evolution Equations and Control Theory
language:
Short-container-title:EECT

Author:

Alahyane Mohamed¹,Al-Gharabli Mohammad M.²³,M. Al-Mahdi Adel²³

Affiliation:

1. Arts et Metiers Institute of Technology, Centrale Lille, Junia, ULR2697 - L2EP, University of Lille, France

2. The Preparatory Year Program, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

3. IRC for construction and building materials, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Abstract

<p style='text-indent:20px;'>In this paper, we consider a one-dimensional linear Bresse system with only one infinite memory term acting in the third equation (longitudinal displacements). Under a general condition on the memory kernel (relaxation function), we establish a decay estimate of the energy of the system. Our decay result extends and improves some decay rates obtained in the literature such as the one in [<xref ref-type="bibr" rid="b27">27</xref>], [<xref ref-type="bibr" rid="b4">4</xref>], [<xref ref-type="bibr" rid="b33">33</xref>], [<xref ref-type="bibr" rid="b58">58</xref>] and [<xref ref-type="bibr" rid="b34">34</xref>]. The proof is based on the energy method together with convexity arguments. Numerical simulations are given to illustrate the theoretical decay result.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Control and Optimization,Modeling and Simulation

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