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