Stability of the wave equation with localized Kelvin-Voigt damping and boundary delay feedback

Abstract

We study the stabilization problem for the wave equation with localized Kelvin-Voigt damping and mixed boundary condition with time delay. By using a frequency domain approach we show that, under an appropriate condition between the internal damping and the boundary feedback, an exponential stability result holds. In this sense, this extends the result of [19] where, in a more general setting, the case of distributed structural damping is considered.