Journal of Mathematical Physics, Analysis, Geometry
2019, vol. 15, No 3, pp. 412-424   https://doi.org/10.15407/mag15.03.412     ( to contents , go back )
https://doi.org/10.15407/mag15.03.412

Notes on the Asymptotic Properties of Some Class of Unbounded Strongly Continuous Semigroups

G.M. Sklyar

Institute of Mathematics, University of Szczecin, Wielkopolska 15, Szczecin 70-451, Poland
E-mail: sklar@univ.szczecin.pl

P. Polak

Institute of Mathematics, University of Szczecin, Wielkopolska 15, Szczecin 70-451, Poland
E-mail: piotr.polak@usz.edu.pl

Received April 4, 2018.

Abstract

The abstract Cauchy problem in the Banach and Hilbert space setting is considered and the asymptotic behavior of individual orbits of corresponding C0-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.

Mathematics Subject Classification 2000: 34K20, 35B40, 93D20.
Key words: linear differential equations, asymptotic behavior of solutions, maximal asymptotics, asymptotic stability, polynomial stability.

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