Geodesic
Optimal regularization method for ill-posed Cauchy problems
Electronic journal of differential equations, Tome 2006 (2006)
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.
Classification : 35K90, 47D06, 47A52, 35R25
Keywords: ill-posed Cauchy problem, quasi-reversibility method, nonlocal conditions, regularizing family 
@article{EJDE_2006__2006__a160,
     author = {Boussetila,  Nadjib and Rebbani,  Faouzia},
     title = {Optimal regularization method for ill-posed {Cauchy} problems},
     journal = {Electronic journal of differential equations},
     year = {2006},
     volume = {2006},
     zbl = {1112.35336},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a160/}
}
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Boussetila,  Nadjib; Rebbani,  Faouzia. Optimal regularization method for ill-posed Cauchy problems. Electronic journal of differential equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a160/