A Modified Quasi-Reversibility Method for a Class of Ill-Posed Cauchy Problems

Author:

Boussetila Nadjib1,Rebbani Faouzia1

Affiliation:

1. Applied Math Lab., University Badji Mokhtar-Annaba, P.O.Box. 12, Annaba 23000, Algeria. E-mail:

Abstract

Abstract The goal of this paper is to present some extensions of the method of quasi-reversibility applied to an ill-posed Cauchy problem associated with an unbounded linear operator in a Hilbert space. The key point to our proof is the use of a new perturbation to construct a family of regularizing operators for the considered problem. We show the convergence of this method, and we estimate the convergence rate under a priori regularity assumptions on the problem data.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

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