Journal of Dynamical and Control Systems

, Volume 23, Issue 2, pp 237–247 | Cite as

Uniform Stabilization of an Axially Moving Kirchhoff String by a Boundary Control of Memory Type

  • Abdelkarim Kelleche
  • Nasser-eddine Tatar
  • Ammar Khemmoudj
Article

Abstract

In this paper, we study the stabilization of solutions of an axially moving string of kirchhoff type by a viscoelastic boundary control. We prove that the dissipation produced by the viscoelastic term is sufficient to suppress the transversal vibrations that occur during the axial motion of the string, and we also show that the string displacement decays in an arbitrary rate. When comparing with immobile strings, we conclude that the movement of the string itself produces enough extra damping ensuring the stabilization.

Keywords

Kirchhoff string Axial motion Boundary control of memory type Arbitrary decay 

Mathematics Subject Classification (2010)

35L20 35B40 45K05 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Faculté des MathématiquesUniversité des Sciences et de la Technologie Houari BoumedieneAlgerAlgeria
  2. 2.Department of Mathematics and StatisticsKing Fahd University of Petroleum and MineralsDhahranSaudi Arabia

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