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Multiscale Lavrentiev method for systems of Volterra equations of the first kind
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A. Favini
Veröffentlicht/Copyright:
26. Mai 2008
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.
Published Online: 2008-05-26
Published in Print: 2008-May
© de Gruyter 2008
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Artikel in diesem Heft
- Inverse problem for parabolic high-order equations
- Multiscale Lavrentiev method for systems of Volterra equations of the first kind
- Recovering memory kernels in parabolic transmission problems
- Impact of conditional stability: Convergence rates for general linear regularization methods
- Differential identities and uniqueness theorem in inverse problem for the Boltzmann–Vlasov equation
- Inverse problem with unknown composite external action for hyperbolic equations
Schlagwörter für diesen Artikel
Volterra integral equations of first kind;
Lavrentiev method;
regularization
Artikel in diesem Heft
- Inverse problem for parabolic high-order equations
- Multiscale Lavrentiev method for systems of Volterra equations of the first kind
- Recovering memory kernels in parabolic transmission problems
- Impact of conditional stability: Convergence rates for general linear regularization methods
- Differential identities and uniqueness theorem in inverse problem for the Boltzmann–Vlasov equation
- Inverse problem with unknown composite external action for hyperbolic equations
