Well-posedness and exponential stability for the logarithmic Lamé system with a time delay

Hazal Yüksekkaya; Erhan Piskin; Mohammad M. Kafini; Adel M. Al-Mahdi

doi:10.1080/00036811.2023.2196993

Well-posedness and exponential stability for the logarithmic Lamé system with a time delay

Hazal Yüksekkaya
, Erhan Piskin
, Mohammad M. Kafini
, Adel M. Al-Mahdi^*

^*Corresponding author for this work

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

11 Scopus citations

Abstract

This paper is concerned with the initial-boundary value problem for a logarithmic Lamé system with a time delay in a bounded domain. We prove the well-posedness of the system by utilizing the semigroup theory. Then, we prove the existence of global solutions by using the well-depth method. In addition, we establish an exponential stability decay result under appropriate assumptions on the weight of the time delay and that of frictional damping.

Original language	English
Pages (from-to)	506-518
Number of pages	13
Journal	Applicable Analysis
Volume	103
Issue number	2
DOIs	https://doi.org/10.1080/00036811.2023.2196993
State	Published - 2024

Bibliographical note

Publisher Copyright:
© 2023 Informa UK Limited, trading as Taylor & Francis Group.

Keywords

Logarithmic Lamé system
delay term
exponential stability
global existence

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1080/00036811.2023.2196993

Cite this

@article{ac89d10363204dc6979afb6f4c64fef8,

title = "Well-posedness and exponential stability for the logarithmic Lam{\'e} system with a time delay",

abstract = "This paper is concerned with the initial-boundary value problem for a logarithmic Lam{\'e} system with a time delay in a bounded domain. We prove the well-posedness of the system by utilizing the semigroup theory. Then, we prove the existence of global solutions by using the well-depth method. In addition, we establish an exponential stability decay result under appropriate assumptions on the weight of the time delay and that of frictional damping.",

keywords = "Logarithmic Lam{\'e} system, delay term, exponential stability, global existence",

author = "Hazal Y{\"u}ksekkaya and Erhan Piskin and Kafini, \{Mohammad M.\} and Al-Mahdi, \{Adel M.\}",

note = "Publisher Copyright: {\textcopyright} 2023 Informa UK Limited, trading as Taylor \& Francis Group.",

year = "2024",

doi = "10.1080/00036811.2023.2196993",

language = "English",

volume = "103",

pages = "506--518",

journal = "Applicable Analysis",

issn = "0003-6811",

number = "2",

}

TY - JOUR

T1 - Well-posedness and exponential stability for the logarithmic Lamé system with a time delay

AU - Yüksekkaya, Hazal

AU - Piskin, Erhan

AU - Kafini, Mohammad M.

AU - Al-Mahdi, Adel M.

PY - 2024

Y1 - 2024

N2 - This paper is concerned with the initial-boundary value problem for a logarithmic Lamé system with a time delay in a bounded domain. We prove the well-posedness of the system by utilizing the semigroup theory. Then, we prove the existence of global solutions by using the well-depth method. In addition, we establish an exponential stability decay result under appropriate assumptions on the weight of the time delay and that of frictional damping.

AB - This paper is concerned with the initial-boundary value problem for a logarithmic Lamé system with a time delay in a bounded domain. We prove the well-posedness of the system by utilizing the semigroup theory. Then, we prove the existence of global solutions by using the well-depth method. In addition, we establish an exponential stability decay result under appropriate assumptions on the weight of the time delay and that of frictional damping.

KW - Logarithmic Lamé system

KW - delay term

KW - exponential stability

KW - global existence

UR - https://www.scopus.com/pages/publications/85151430221

U2 - 10.1080/00036811.2023.2196993

DO - 10.1080/00036811.2023.2196993

M3 - Article

AN - SCOPUS:85151430221

SN - 0003-6811

VL - 103

SP - 506

EP - 518

JO - Applicable Analysis

JF - Applicable Analysis

IS - 2

ER -

Well-posedness and exponential stability for the logarithmic Lamé system with a time delay

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this