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Existence and exponential stability of a damped wave equation with dynamic boundary conditions and a delay term. (English) Zbl 1278.35147

Summary: We consider a multi-dimensional wave equation with dynamic boundary conditions related to the Kelvin-Voigt damping and a delay term acting on the boundary. If the weight of the delay term in the feedback is less than the weight of the term without delay or if it is greater under an assumption between the damping factor, and the difference of the two weights, we prove the global existence of the solutions. Under the same assumptions, the exponential stability of the system is proved using an appropriate Lyapunov functional. More precisely, we show that even when the weight of the delay is greater than the weight of the damping in the boundary conditions, the strong damping term still provides exponential stability for the system.

MSC:

35L35 Initial-boundary value problems for higher-order hyperbolic equations
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35B35 Stability in context of PDEs
35R10 Partial functional-differential equations
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