Feedback stabilization of a coupled string-beam system

Kaïs Ammari 1 Mohamed Jellouli 2 Michel Mehrenberger 3, 4
3 CALVI - Scientific computation and visualization
IRMA - Institut de Recherche Mathématique Avancée, LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection, Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine
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.
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Networks and Heterogeneous Media, AIMS-American Institute of Mathematical Sciences, 2009, 〈10.3934/nhm.2009.4.19〉
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https://hal.archives-ouvertes.fr/hal-01298964
Contributeur : Michel Mehrenberger <>
Soumis le : mercredi 6 avril 2016 - 21:02:30
Dernière modification le : mercredi 14 mars 2018 - 16:42:15

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Kaïs Ammari, Mohamed Jellouli, Michel Mehrenberger. Feedback stabilization of a coupled string-beam system. Networks and Heterogeneous Media, AIMS-American Institute of Mathematical Sciences, 2009, 〈10.3934/nhm.2009.4.19〉. 〈hal-01298964〉

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