Electron. J. Diff. Eqns., Vol. 2006(2006), No. 147, pp. 1-15.

Optimal regularization method for ill-posed Cauchy problems

Nadjib Boussetila, Faouzia Rebbani

Abstract:
The goal of this paper is to give an optimal regularization method for an ill-posed Cauchy problem associated with an unbounded linear operator in a Hilbert space. Key point to our proof is the use of Yosida approximation and nonlocal conditions to construct a family of regularizing operators for the considered problem. We show the convergence of this approach, and we estimate the convergence rate under a priori regularity assumptions on the problem data.

Submitted February 28, 2006. Published November 27, 2006.
Math Subject Classifications: 35K90, 47D06, 47A52, 35R25.
Key Words: Ill-posed Cauchy problem; quasi-reversibility method; nonlocal conditions; regularizing family.

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Nadjib Boussetila
Applied Math Lab, University Badji Mokhtar-Annaba
P.O. Box 12, Annaba 23000, Algeria
email: naboussetila@yahoo.fr
Faouzia Rebbani
Applied Math Lab, University Badji Mokhtar-Annaba
P.O. Box 12, Annaba 23000, Algeria
email: rebbani@wissal.dz

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