This article is cited in 6 papers

Notes on the asymptotic properties of some class of unbounded strongly continuous semigroups

G. M. Sklyar, P. Polak

Institute of Mathematics, University of Szczecin, Wielkopolska 15, Szczecin 70-451, Poland

Abstract: The abstract Cauchy problem in the Banach and Hilbert space setting is considered and the asymptotic behavior of individual orbits of corresponding $C_0$-semigroup is studied. The possibility to find uniformly stable dense subset of initial states in the case of unstable semigroups (so-called polynomial stability) is discussed. Also, the existence of the fastest growing orbit (so-called maximal asymptotics) for certain class of semigroups is studied.

Key words and phrases: linear differential equations, asymptotic behavior of solutions, maximal asymptotics, asymptotic stability, polynomial stability.

MSC: 34K20, 35B40, 93D20.

Received: 04.04.2018

Language: English

DOI: 10.15407/mag15.03.412

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