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Applicable Analysis
An International Journal
Volume 87, 2008 - Issue 1
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Original Articles

A specific inverse problem for the Volterra convolution equation

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Pages 59-81 | Accepted 04 Jun 2007, Published online: 22 Jan 2008
 

Abstract

This article attends to the specific inverse problem of determining the difference kernel k of a second kind linear Volterra integral equation of convolution type from a prescribed quotient μ of resolvent r and kernel k of the equation. A problem of this type arises, for example, in the theory of viscoelasticity and leads to a nonlinear integral equation of the third kind , for which several existence theorems are proved. Moreover, the applicability of Tikhonov's regularization method is studied. Finally, the case of non-convolution Volterra equations is also briefly discussed.

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