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

Salah-Eddine Rebiai* and Fatima Zohra Sidi Ali

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 strongly continuous 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.

Mathematics Subject Classification: 35L05 93D15

Keywords: Coupled wave equations; time delays; boundary stabilization.

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