On a Kelvin-Voigt viscoelasticwave equation with strong delay

An initial-boundary value problem for a viscoelastic wave equation subject to a strong timelocalized
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.