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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year


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Online
ISSN
1569-3945
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In This Section
Volume 16, Issue 3 (Jan 2008)

Issues

Multiscale Lavrentiev method for systems of Volterra equations of the first kind

A. Favini / L. Pandolfi
Published Online: 2008-05-26 | DOI: https://doi.org/10.1515/JIIP.2008.014

Abstract

We study the singular perturbation approach proposed by Lavrentiev for the regularization of systems of Volterra integral equations of the first kind, in the case that the kernel K(t) is not invertible for t = 0 and without assuming K(t) ~ t v I. We single out a class of kernels, which we call “diagonally dominant”. We show that when the kernel belongs to this class then it is possible to regularize the problem using a multiscale singular perturbation method.

Key words.: Volterra integral equations of first kind; Lavrentiev method; regularization

About the article

A. Favini, University of Bologna, Department of Mathematics, Piazza di Porta San Donato 5, Bologna, Italy. Email:

L. Pandolfi, Politecnico di Torino, Dipartimento di Matematica, Corso Duca degli Abruzzi 24, 10129 Torino, Italy. Email:


Published Online: 2008-05-26

Published in Print: 2008-05-01



Citation Information: Journal of Inverse and Ill-posed Problems, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/JIIP.2008.014. Export Citation

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Luciano Pandolfi
Annual Reviews in Control, 2010, Volume 34, Number 2, Page 245
[2]
A. Favini and L. Pandolfi
Numerical Functional Analysis and Optimization, 2008, Volume 29, Number 11-12, Page 1252
[3]
Luciano Pandolfi
Discrete and Continuous Dynamical Systems - Series S, 2010, Volume 4, Number 3, Page 745

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