Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 147, pp. 1-15.

Title: Optimal regularization method for ill-posed Cauchy problems

Authors: Nadjib Boussetila (Univ. Badji Mokhtar-Annaba, Algeria)
         Faouzia Rebbani   (Univ. Badji Mokhtar-Annaba, Algeria)
	 
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.
 
Submitted February 28, 2006. Published November 27, 2006.
Math Subject Classifications: 35K90, 47D06, 47A52, 35R25.
Key Words: Ill-posed Cauchy problem; quasi-reversibility method;
           nonlocal conditions; regularizing family.