Optimal regularization method for ill-posed Cauchy problems. (English) Zbl 1112.35336

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.


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
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