A new approach to the stability of an abstract system in the presence of infinite history

A. Guesmia; S. A. Messaoudi

doi:10.1016/j.jmaa.2014.02.030

A new approach to the stability of an abstract system in the presence of infinite history

A. Guesmia^*, S. A. Messaoudi

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

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

49 Scopus citations

Abstract

In this paper, we consider the following problem, where A is a self-adjoint positive definite operator and g is a positive nonincreasing function. We adopt the method introduced in [19], for finite history, with some modifications imposed by the nature of our problem, to establish a general decay result which depends only on the behavior of the relaxation function. Our result extends the decay result obtained for problems with finite history to those with infinite history. In addition, it improves, in some cases, some decay results obtained earlier in [15].

Original language	English
Pages (from-to)	212-228
Number of pages	17
Journal	Journal of Mathematical Analysis and Applications
Volume	416
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2014.02.030
State	Published - 1 Aug 2014

Bibliographical note

Funding Information:
The authors thank KFUPM for its continuous support. This work has been funded by KFUPM under project # FT121007 .

Keywords

General decay
Infinite history
Viscoelasticity

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1016/j.jmaa.2014.02.030

Cite this

@article{11dfb19d47944196852f3ba2115fa20b,

title = "A new approach to the stability of an abstract system in the presence of infinite history",

abstract = "In this paper, we consider the following problem, where A is a self-adjoint positive definite operator and g is a positive nonincreasing function. We adopt the method introduced in [19], for finite history, with some modifications imposed by the nature of our problem, to establish a general decay result which depends only on the behavior of the relaxation function. Our result extends the decay result obtained for problems with finite history to those with infinite history. In addition, it improves, in some cases, some decay results obtained earlier in [15].",

keywords = "General decay, Infinite history, Viscoelasticity",

author = "A. Guesmia and Messaoudi, \{S. A.\}",

note = "Funding Information: The authors thank KFUPM for its continuous support. This work has been funded by KFUPM under project \# FT121007 .",

year = "2014",

month = aug,

day = "1",

doi = "10.1016/j.jmaa.2014.02.030",

language = "English",

volume = "416",

pages = "212--228",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

number = "1",

}

TY - JOUR

T1 - A new approach to the stability of an abstract system in the presence of infinite history

AU - Guesmia, A.

AU - Messaoudi, S. A.

N1 - Funding Information: The authors thank KFUPM for its continuous support. This work has been funded by KFUPM under project # FT121007 .

PY - 2014/8/1

Y1 - 2014/8/1

N2 - In this paper, we consider the following problem, where A is a self-adjoint positive definite operator and g is a positive nonincreasing function. We adopt the method introduced in [19], for finite history, with some modifications imposed by the nature of our problem, to establish a general decay result which depends only on the behavior of the relaxation function. Our result extends the decay result obtained for problems with finite history to those with infinite history. In addition, it improves, in some cases, some decay results obtained earlier in [15].

AB - In this paper, we consider the following problem, where A is a self-adjoint positive definite operator and g is a positive nonincreasing function. We adopt the method introduced in [19], for finite history, with some modifications imposed by the nature of our problem, to establish a general decay result which depends only on the behavior of the relaxation function. Our result extends the decay result obtained for problems with finite history to those with infinite history. In addition, it improves, in some cases, some decay results obtained earlier in [15].

KW - General decay

KW - Infinite history

KW - Viscoelasticity

UR - https://www.scopus.com/pages/publications/84897098064

U2 - 10.1016/j.jmaa.2014.02.030

DO - 10.1016/j.jmaa.2014.02.030

M3 - Article

AN - SCOPUS:84897098064

SN - 0022-247X

VL - 416

SP - 212

EP - 228

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

A new approach to the stability of an abstract system in the presence of infinite history

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this