Perturbation theory for dual semigroups II. Time-dependent perturbations in the sun-reflexive case

Ph Clement, O. Diekmann, M. Gyllenberg, H. J.A.M. Heijmans, H. R. Thieme

Research output: Contribution to journalArticle

22 Scopus citations

Abstract

We consider time-dependent perturbations of generators of strongly continuous semigroups on a Banach space. The perturbations map the Banach space into a bigger space, which is the second dual of the original space in a specific semigroup sense. Using the theory of dual semigroups we show that the solutions of a generalised variation-of-constants formula define an evolutionary system. We investigate continuity and differentiability properties of this evolutionary system and its dual system and examine in what sense the perturbed generator and its adjoint generate these evolutionary systems. It is shown that the results apply naturally to retarded functional differential equations and age structured population dynamics.

Original languageEnglish (US)
Pages (from-to)145-172
Number of pages28
JournalProceedings of the Royal Society of Edinburgh: Section A Mathematics
Volume109
Issue number1-2
DOIs
StatePublished - Jan 1 1988

ASJC Scopus subject areas

  • Mathematics(all)

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