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

• Published in: Applied mathematics letters Vol. 24; no. 1; pp. 71 - 75
• Main Authors: Anderssen, R.S., Davies, A.R., de Hoog, F.R.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 2011; Elsevier
• Subjects: Approximation; Assessments; Convolution; Creep (materials); Exact sciences and technology; First-kind Volterra integral equation; Integral equations; Interconversion; Kernel perturbations; Kernels; Linear viscoelasticity; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Perturbation methods; Sciences and techniques of general use; Interconversion; Convolution; Linear viscoelasticity; Kernel perturbations; First-kind Volterra integral equation; Viscoelasticity; Approximation; Linear equation; Convolution equation; Applied mathematics; Well posed problem; Volterra integral equations
• ISSN: 0893-9659; 1873-5452
• DOI: 10.1016/j.aml.2010.08.019

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 .