Regularization for a class of ill-posed Cauchy problems

Abstract

This paper is concerned with the ill-posed Cauchy problem associated with a densely defined linear operator A A in a Banach space. Our main result is that if − A -A is the generator of an analytic semigroup of angle ≥ π / 4 \ge \pi /4 , then there exists a family of regularizing operators for such an ill-posed Cauchy problem by using the Gajewski and Zacharias quasi-reversibility method, and semigroups of linear operators.