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