Том 230, № 4 (2018)

In this survey, some interesting generalizations of the theory of C₀-semigroups and their applications are presented. The survey is divided into three parts: “Integrated semigroups,” “C-semigroups,” and “Applications.” Different approaches to the theory are discussed. The content presented is taken from articles of the last 20 years and also contains some results of the authors. Various applications are presented; most of them concern ill-posed Cauchy problems.