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Feedback boundary stabilization of wave equations with interior delay. (English) Zbl 1205.93126

Summary: We consider a boundary stabilization problem for the wave equation with interior delay. We prove an exponential stability result under some Lions’ geometric condition. The proof of the main result is based on an identity with multipliers that allows us to obtain a uniform decay estimate for a suitable Lyapunov functional.

MSC:

93D20 Asymptotic stability in control theory
93C20 Control/observation systems governed by partial differential equations
35Q93 PDEs in connection with control and optimization
93C25 Control/observation systems in abstract spaces
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