Feedback stabilization of a coupled string-beam system

Kaïs Ammari; Mohamed Jellouli; Michel Mehrenberger

doi:10.3934/nhm.2009.4.19

Article Contents

2009, Volume 4, Issue 1: 19-34. Doi: 10.3934/nhm.2009.4.19

This issue Previous Article Self--motion of camphor discs. model and analysis Next Article A uniformly second order numerical method for the one-dimensional discrete-ordinate transport equation and its diffusion limit with interface

Feedback stabilization of a coupled string-beam system

1.
Département de Mathématiques, Faculté des Sciences de Monastir, 5019 Monastir
2.
Institut de Recherche Mathématique Avancée, Université Louis Pasteur, 7, rue René Descartes, 67084 Strasbourg

Received: December 2007

Revised: September 2008

Published: March 2009

Abstract / Introduction Related Papers Cited by

Abstract

We consider a stabilization problem for a coupled string-beam system. We prove some decay results of the energy of the system. The method used is based on the methodology introduced in Ammari and Tucsnak [2] where the exponential and weak stability for the closed loop problem is reduced to a boundedness property of the transfer function of the associated open loop system. Morever, we prove, for the same model but with two control functions, independently of the length of the beam that the energy decay with a polynomial rate for all regular initial data. The method used, in this case, is based on a frequency domain method and combine a contradiction argument with the multiplier technique to carry out a special analysis for the resolvent.

Keywords:

Mathematics Subject Classification: Primary: 93B07, 35M10, 35A25; Secondary: 42A16.

Citation:

Article Metrics

HTML views() PDF downloads(155) Cited by(0)

Feedback stabilization of a coupled string-beam system

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Feedback stabilization of a coupled string-beam system

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content