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
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
- Published Online:
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.
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