On shape preserving semigroups (Q663179)

In this paper the authors introduce a definition of shape-preserving operator semigroups that improves a previous definition due to \textit{M. Kovács} [J. Math. Anal. Appl. 304, No.~1, 115--136 (2005; Zbl 1068.47050)] and analyze their fundamental properties. The authors establish sufficient conditions for shape-preservability of semigroups under approximations and perturbations. The theoretical results are illustrated by some examples and the paper ends with an application to partial differential delay equations.