Boussetila, Nadjib; Rebbani, Faouzia Optimal regularization method for ill-posed Cauchy problems. (English) Zbl 1112.35336 Electron. J. Differ. Equ. 2006, Paper No. 147, 15 p. (2006). Summary: 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. Cited in 2 ReviewsCited in 7 Documents MSC: 35K90 Abstract parabolic equations 47D06 One-parameter semigroups and linear evolution equations 47A52 Linear operators and ill-posed problems, regularization 35R25 Ill-posed problems for PDEs Keywords:quasi-reversibility method; nonlocal conditions; regularizing family PDFBibTeX XMLCite \textit{N. Boussetila} and \textit{F. Rebbani}, Electron. J. Differ. Equ. 2006, Paper No. 147, 15 p. (2006; Zbl 1112.35336) Full Text: EuDML EMIS