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 proceedingConference contributionpeer-review

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 languageEnglish
Title of host publicationProceedings of the 2017 International Conference on Mathematics and Information Technology, ICMIT 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages384-389
Number of pages6
ISBN (Electronic)9781538632680
DOIs
StatePublished - 1 Jul 2017

Publication series

NameProceedings of the 2017 International Conference on Mathematics and Information Technology, ICMIT 2017
Volume2018-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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