Optimal regularization method for ill-posed Cauchy problems

Date

2006-11-27

Authors

Boussetila, Nadjib
Rebbani, Faouzia

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University-San Marcos, Department of Mathematics

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.

Description

Keywords

Ill-posed Cauchy problem, Quasi-reversibility methods, Nonlocal conditions, Regularizing family

Citation

Boussetila, N., & Rebbani, F. (2006). Optimal regularization method for ill-posed Cauchy problems. <i>Electronic Journal of Differential Equations, 2006</i>(147), pp. 1-15.

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Attribution 4.0 International

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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