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

Anderssen, R. S., Davies, Arthur Russell and de Hoog, F. R. 2011. The effect of kernel perturbations when solving the interconversion convolution equation of linear viscoelasticity. Applied Mathematics Letters 24 (1) , pp. 71-75. 10.1016/j.aml.2010.08.019

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Abstract

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. 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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Linear viscoelasticity; Interconversion; Kernel perturbations; Convolution; First-kind Volterra integral equation
Publisher:	Elsevier
ISSN:	0893-9659
Last Modified:	04 Jun 2017 02:55
URI:	https://orca.cardiff.ac.uk/id/eprint/13810

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