On the stability of asymptotic properties of perturbed C 0-semigroups
Valentina Casarino, Susanna Piazzera ยท Forum Mathematicum ยท 2001
We give conditions on a strongly continuous semigroup ๐ฏ and an unbounded perturbation B in the class of Miyadera-Voigt such that the perturbed semigroup ๐ฎ inherits asymptotic properties of ๐ฏ as boundedness, asymptotic almost periodicity, uniform ergodicity and total uniform ergodicity. A systematic application of the abstract result to partial differential equations with delay is made.