Etude de certaines classes de problèmes de Cauchy non correctement posés au sens d'Hadamard-Petrovski

Abstract

This work is concerned the study of a class of ill-posed Cauchy problems associated with a densely defined linear operator A in a Banach space X. It is proved that if –A is the generator of an analytic semi-group, then there exists a family of regularizing operators by using the quasi-reversibility method, fractional powers and semi-groups of linear operators.