A MODIFIED QUASI-REVERSIBILITY METHOD FOR A CLASS OF ILL-POSED CAUCHY PROBLEMS

Abstract. The goal of this paper is to present some extensions of the method of quasi-reversibility applied to an ill-posed Cauchy problem associated with an unbounded linear operator in a Hilbert space. The key point to our proof is the use of a new perturbation to construct a family of regularizing operators for the considered problem. We show the convergence of this method, and we estimate the convergence rate under a priori regularity assumptions on the problem data