# Exponential Stability of Compactly Coupled Wave Equations with Delay Terms in the Boundary Feedbacks

Abstract : We consider a linear system of compactly coupled wave equations with Neumann feedback controllers that contain delay terms. First, we prove under some assumptions that the closed-loop system generates a $C_{0}-$semigroup of contractions on an appropriate Hilbert space. Then, under further assumptions, we show that the closed-loop system is exponentially stable. This result is obtained by introducing a suitable energy function and by using an observability estimate.
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Communication dans un congrès
Christian Pötzsche; Clemens Heuberger; Barbara Kaltenbacher; Franz Rendl. 26th Conference on System Modeling and Optimization (CSMO), Sep 2013, Klagenfurt, Austria. Springer Berlin Heidelberg, IFIP Advances in Information and Communication Technology, AICT-443, pp.278-284, 2014, System Modeling and Optimization. 〈10.1007/978-3-662-45504-3_27〉
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https://hal.inria.fr/hal-01286436
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Salah-Eddine Rebiai, Fatima Sidi Ali. Exponential Stability of Compactly Coupled Wave Equations with Delay Terms in the Boundary Feedbacks. Christian Pötzsche; Clemens Heuberger; Barbara Kaltenbacher; Franz Rendl. 26th Conference on System Modeling and Optimization (CSMO), Sep 2013, Klagenfurt, Austria. Springer Berlin Heidelberg, IFIP Advances in Information and Communication Technology, AICT-443, pp.278-284, 2014, System Modeling and Optimization. 〈10.1007/978-3-662-45504-3_27〉. 〈hal-01286436〉

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