ON A KELVIN-VOIGT VISCOELASTIC WAVE EQUATION WITH STRONG DELAY

An initial-boundary value problem for a viscoelastic wave equation subject to a strong time-localized delay in a Kelvin-Voigt-type material law is considered. After transforming the equation to an abstract Cauchy problem on the extended phase space, a global well-posedness theory is established using the operator semigroup theory both in Sobolev-valued C-0- and BV-spaces. Under appropriate assumptions on the coefficients, a global exponential decay rate is obtained and the stability region in the parameter space is further explored using Lyapunov's indirect method. The singular limit tau -> 0 is studied with the aid of the energy method. Finally, a numerical example from a real-world application in biomechanics is presented.