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. 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 C0- 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 the Lyapunov's indirect method. The singular limit τ→0 is
further studied with the aid of the energy method. Finally, a numerical example
from a real-world application in biomechanics is presented.Comment: 34 pages, 4 figures, 1 set of Matlab code