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In this paper we consider a multi-dimensional wave equation with dynamicboundary conditions related to the Kelvin-Voigt damping and a delay term actingon the boundary. If the weight of the delay term in the feedback is less thanthe weight of the term without delay or if it is greater under an assumptionbetween the damping factor, and the difference of the two weights, we prove theglobal existence of the solutions. Under the same assumptions, the exponentialstability of the system is proved using an appropriate Lyapunov functional.More precisely, we show that even when the weight of the delay is greater thanthe weight of the damping in the boundary conditions, the strong damping termstill provides exponential stability for the system.

Existence and exponential stability of a damped wave equation with dynamic boundary conditions and a delay term