Uniformly stable approximation for a linear viscoelastic model

AbstractWe consider an equation arising in linear viscoelasticity. Recently it has been shown that the semigroup for this model is exponentially stable, and that a certain semidiscrete approximation scheme preserves the stability uniformly in the discretization parameter. However, that uniform stability result requires two technical assumptions, which have been verified only for a limited class of viscoelastic kernel functions. In this note, we show that one assumption is unnecessary, and the other follows from a simple additional assumption on the kernel, which is easily verified for a large class of functions