Boussetila, NadjibRebbani, Faouzia2021-07-212021-07-212006-11-27Boussetila, N., & Rebbani, F. (2006). Optimal regularization method for ill-posed Cauchy problems. <i>Electronic Journal of Differential Equations, 2006</i>(147), pp. 1-15.1072-6691https://hdl.handle.net/10877/14020The 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.Text15 pages1 file (.pdf)enAttribution 4.0 InternationalIll-posed Cauchy problemQuasi-reversibility methodsNonlocal conditionsRegularizing familyArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.