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Boundary feedback stabilization of a chain of serially connected strings

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  • We consider $N$ strings connected one to another and forming a particular network which is a chain of strings. We study a stabilization problem and precisely we prove that the energy of the solutions of the dissipative system decays exponentially to zero when the time tends to infinity, independently of the densities of the strings. Our technique is based on a frequency domain method and a special analysis for the resolvent. Moreover, by the same approach, we study the transfer function associated to the chain of strings and the stability of the Schrödinger system.
    Mathematics Subject Classification: Primary: 35L05, 35M10; Secondary: 35R02, 47A10, 93D15, 93D20.


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