## JMI2012A-1 Kernel perturbations for convolution first kind Volterra integral equations (pp.1-4)

Author(s)： Frank R. de Hoog and Robert S. Anderssen

J. Math-for-Ind. **4A** (2012) 1-4.

- File： JMI2012A-1.pdf (91KB)

Abstract

Because of their causal structure, (convolution) Volterra integral equations arise as models in a variety of real-world situations including rheological stress-strain analysis, population dynamics and insurance risk prediction. In such practical situations, often only an approximation for the kernel is available. Consequently, a key aspect in the analysis of such equations is estimating the effect of kernel perturbations on the solutions. In this paper, it is shown how kernel perturbation results derived for the interconversion equation of rheology can be extended to the analysis of kernel perturbations for first kind convolutional integral equations with positive kernels, solutions and forcing terms.

Keyword(s). linear viscoelasticity, interconversion, kernel perturbations, convolution, first kind Volterra integral equations