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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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

A. Favini / L. Pandolfi

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:

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 16, Issue 3, Pages 221–238, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/JIIP.2008.014, May 2008

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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

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