The effect of kernel perturbations when solving the interconversion convolution equation of linear viscoelasticity

In the study of linear viscoelastic materials, from measurements of the relaxation modulus G(t)G(t), approximations to the corresponding creep compliance (retardation) modulus J(t)J(t) are determined by solving the convolution interconversion equation ∫0tJ(t−s)G(s)ds=t,t⩾0. By taking explicit account of the fact that G(t)G(t) is a positive decreasing function, which automatically guarantees that J(t)J(t) is positive increasing, new estimates are derived for the effect of perturbation in GG on JJ. They allow an explicit assessment to be made of the well-posedness of the recovery of JJ from an approximation to GG.