Geodesic
Integrated Semigroups and $C$-Semigroups and Their Applications
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Functional analysis, Tome 131 (2017), pp. 3-109

Voir la notice de l'article provenant de la source Math-Net.Ru

In this survey, some interesting generalizations of the theory of $C_0$-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; the most of them concerns ill-posed Cauchy problems.
Keywords: semigroup, integrated semigroup, $C$-semigroup, Cauchy problem, differential equation. 
@article{INTO_2017_131_a0,
     author = {V. V. Vasil'ev and S. I. Piskarev and N. Yu. Selivanova},
     title = {Integrated {Semigroups} and $C${-Semigroups} and {Their} {Applications}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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     publisher = {mathdoc},
     volume = {131},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_131_a0/}
}
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V. V. Vasil'ev; S. I. Piskarev; N. Yu. Selivanova. Integrated Semigroups and $C$-Semigroups and Their Applications. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Functional analysis, Tome 131 (2017), pp. 3-109. http://geodesic.mathdoc.fr/item/INTO_2017_131_a0/