Existence and stabilization of a Kirchhoff moving string with a distributed delay in the internal feedback

Abdelkarim Kelleche; Nasser Eddine Tatar

doi:10.1109/MATHIT.2017.8259746

Existence and stabilization of a Kirchhoff moving string with a distributed delay in the internal feedback

Abdelkarim Kelleche^*, Nasser Eddine Tatar

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

In this article, we are concerned by the study of the effect of a distributed time-delay in internal stabilization of a moving string. The model adopted here is nonlinear and of 'Kirchhoff' type. We prove the well-posedness of the system by exploiting of the Faedo-Galerkin method. We prove that the solution of the system approaches the equilibrium in an exponential manner in the energy norm. To this end we request that the delayed term be dominated by the damping term. This is established through the multiplier technique.

Original language	English
Title of host publication	Proceedings of the 2017 International Conference on Mathematics and Information Technology, ICMIT 2017
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	384-389
Number of pages	6
ISBN (Electronic)	9781538632680
DOIs	https://doi.org/10.1109/MATHIT.2017.8259746
State	Published - 1 Jul 2017

Publication series

Name	Proceedings of the 2017 International Conference on Mathematics and Information Technology, ICMIT 2017
Volume	2018-January

Bibliographical note

Publisher Copyright:
© 2017 IEEE.

Keywords

Axially moving string
Internal delay term
distributed delay
exponential stability

ASJC Scopus subject areas

Computer Networks and Communications
Computer Vision and Pattern Recognition
Signal Processing
Decision Sciences (miscellaneous)
Computational Mathematics
Modeling and Simulation
Numerical Analysis

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10.1109/MATHIT.2017.8259746

Cite this

Kelleche, A., & Tatar, N. E. (2017). Existence and stabilization of a Kirchhoff moving string with a distributed delay in the internal feedback. In Proceedings of the 2017 International Conference on Mathematics and Information Technology, ICMIT 2017 (pp. 384-389). (Proceedings of the 2017 International Conference on Mathematics and Information Technology, ICMIT 2017; Vol. 2018-January). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/MATHIT.2017.8259746

Kelleche, Abdelkarim ; Tatar, Nasser Eddine. / Existence and stabilization of a Kirchhoff moving string with a distributed delay in the internal feedback. Proceedings of the 2017 International Conference on Mathematics and Information Technology, ICMIT 2017. Institute of Electrical and Electronics Engineers Inc., 2017. pp. 384-389 (Proceedings of the 2017 International Conference on Mathematics and Information Technology, ICMIT 2017).

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title = "Existence and stabilization of a Kirchhoff moving string with a distributed delay in the internal feedback",

abstract = "In this article, we are concerned by the study of the effect of a distributed time-delay in internal stabilization of a moving string. The model adopted here is nonlinear and of 'Kirchhoff' type. We prove the well-posedness of the system by exploiting of the Faedo-Galerkin method. We prove that the solution of the system approaches the equilibrium in an exponential manner in the energy norm. To this end we request that the delayed term be dominated by the damping term. This is established through the multiplier technique.",

keywords = "Axially moving string, Internal delay term, distributed delay, exponential stability",

author = "Abdelkarim Kelleche and Tatar, \{Nasser Eddine\}",

note = "Publisher Copyright: {\textcopyright} 2017 IEEE.",

year = "2017",

month = jul,

day = "1",

doi = "10.1109/MATHIT.2017.8259746",

language = "English",

series = "Proceedings of the 2017 International Conference on Mathematics and Information Technology, ICMIT 2017",

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address = "United States",

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Kelleche, A & Tatar, NE 2017, Existence and stabilization of a Kirchhoff moving string with a distributed delay in the internal feedback. in Proceedings of the 2017 International Conference on Mathematics and Information Technology, ICMIT 2017. Proceedings of the 2017 International Conference on Mathematics and Information Technology, ICMIT 2017, vol. 2018-January, Institute of Electrical and Electronics Engineers Inc., pp. 384-389. https://doi.org/10.1109/MATHIT.2017.8259746

Existence and stabilization of a Kirchhoff moving string with a distributed delay in the internal feedback. / Kelleche, Abdelkarim; Tatar, Nasser Eddine.
Proceedings of the 2017 International Conference on Mathematics and Information Technology, ICMIT 2017. Institute of Electrical and Electronics Engineers Inc., 2017. p. 384-389 (Proceedings of the 2017 International Conference on Mathematics and Information Technology, ICMIT 2017; Vol. 2018-January).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Existence and stabilization of a Kirchhoff moving string with a distributed delay in the internal feedback

AU - Kelleche, Abdelkarim

AU - Tatar, Nasser Eddine

PY - 2017/7/1

Y1 - 2017/7/1

N2 - In this article, we are concerned by the study of the effect of a distributed time-delay in internal stabilization of a moving string. The model adopted here is nonlinear and of 'Kirchhoff' type. We prove the well-posedness of the system by exploiting of the Faedo-Galerkin method. We prove that the solution of the system approaches the equilibrium in an exponential manner in the energy norm. To this end we request that the delayed term be dominated by the damping term. This is established through the multiplier technique.

AB - In this article, we are concerned by the study of the effect of a distributed time-delay in internal stabilization of a moving string. The model adopted here is nonlinear and of 'Kirchhoff' type. We prove the well-posedness of the system by exploiting of the Faedo-Galerkin method. We prove that the solution of the system approaches the equilibrium in an exponential manner in the energy norm. To this end we request that the delayed term be dominated by the damping term. This is established through the multiplier technique.

KW - Axially moving string

KW - Internal delay term

KW - distributed delay

KW - exponential stability

UR - https://www.scopus.com/pages/publications/85049469927

U2 - 10.1109/MATHIT.2017.8259746

DO - 10.1109/MATHIT.2017.8259746

M3 - Conference contribution

AN - SCOPUS:85049469927

T3 - Proceedings of the 2017 International Conference on Mathematics and Information Technology, ICMIT 2017

SP - 384

EP - 389

BT - Proceedings of the 2017 International Conference on Mathematics and Information Technology, ICMIT 2017

PB - Institute of Electrical and Electronics Engineers Inc.

ER -

Kelleche A, Tatar NE. Existence and stabilization of a Kirchhoff moving string with a distributed delay in the internal feedback. In Proceedings of the 2017 International Conference on Mathematics and Information Technology, ICMIT 2017. Institute of Electrical and Electronics Engineers Inc. 2017. p. 384-389. (Proceedings of the 2017 International Conference on Mathematics and Information Technology, ICMIT 2017). doi: 10.1109/MATHIT.2017.8259746

Existence and stabilization of a Kirchhoff moving string with a distributed delay in the internal feedback

Abstract

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Keywords

ASJC Scopus subject areas

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