NEW STABILITY RESULT for A BRESSE SYSTEM with ONE INFINITE MEMORY in the SHEAR ANGLE EQUATION

Adel M. Al-Mahdi; Mohammad M. Al-Gharabli; Saeed M. Ali

doi:10.3934/dcdss.2021086

NEW STABILITY RESULT for A BRESSE SYSTEM with ONE INFINITE MEMORY in the SHEAR ANGLE EQUATION

Adel M. Al-Mahdi^*
, Mohammad M. Al-Gharabli
, Saeed M. Ali

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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, g⁰(t) ≤ −ξ(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 η0x. This study generalizes and improves previous literature outcomes.

Original language	English
Pages (from-to)	995-1014
Number of pages	20
Journal	Discrete and Continuous Dynamical Systems - Series S
Volume	15
Issue number	5
DOIs	https://doi.org/10.3934/dcdss.2021086
State	Published - May 2022

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© 2022 American Institute of Mathematical Sciences. All rights reserved.

Keywords

Bress System
Stability
convexity
infinite memory

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcdss.2021086

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title = "NEW STABILITY RESULT for A BRESSE SYSTEM with ONE INFINITE MEMORY in the SHEAR ANGLE EQUATION",

abstract = "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, g0(t) ≤ −ξ(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 η0x. This study generalizes and improves previous literature outcomes.",

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AU - Al-Mahdi, Adel M.

AU - Al-Gharabli, Mohammad M.

AU - Ali, Saeed M.

PY - 2022/5

Y1 - 2022/5

N2 - 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, g0(t) ≤ −ξ(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 η0x. This study generalizes and improves previous literature outcomes.

AB - 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, g0(t) ≤ −ξ(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 η0x. This study generalizes and improves previous literature outcomes.

KW - Bress System

KW - Stability

KW - convexity

KW - infinite memory

UR - https://www.scopus.com/pages/publications/85128258636

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DO - 10.3934/dcdss.2021086

M3 - Article

AN - SCOPUS:85128258636

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VL - 15

SP - 995

EP - 1014

JO - Discrete and Continuous Dynamical Systems - Series S

JF - Discrete and Continuous Dynamical Systems - Series S

IS - 5

ER -

NEW STABILITY RESULT for A BRESSE SYSTEM with ONE INFINITE MEMORY in the SHEAR ANGLE EQUATION

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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