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

摘要

The abstract Cauchy problem in the Banach and Hilbert space setting isconsidered and the asymptotic behavior of individual orbits of correspondingC0-semigroup is studied. The possibility to find uniformly stable densesubset of initial states in the case of unstable semigroups (so-called polynomialstability) is discussed. Also, the existence of the fastest growing orbit(so-called maximal asymptotics) for certain class of semigroups is studied.