``On the stability of asymptotic properties for perturbed C0C_{0}-semigroups'',

We give conditions on a strongly continuous semigroup F and an unbounded perturbation B in the class of Miyadera-Voigt such that the perturbed semigroup. S inherits asymptotic properties of F 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

``On the stability of asymptotic properties for perturbed C0C_{0}-semigroups'',

We give conditions on a strongly continuous semigroup F and an unbounded perturbation B in the class of Miyadera-Voigt such that the perturbed semigroup. S inherits asymptotic properties of F 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

``The asymptotic behaviour of perturbed evolution families'',

We study persistence of asymptotic properties of a semigroup T ( \ub7) on a Banach space X under small, time-varying, closed perturbations B(t) which are relatively bounded with respect to the generator of T ( \ub7). More precisely, it is assumed that the orbits T (\ub7)x belong to a so-called homogeneous subspace E of BU C (R+, X ) (e.g., the space of almost periodic functions) and that a Miyadera-type estimate holds with a small constant. Then the mild solutions of the perturbed Cauchy problem u\u2032 (t) = (A + B(t))u(t), u(0) = x, also belong to E. Further results of a somewhat different nature are proved in the case in which A(t) depends on t, too. The theorems are applied to delay equations

Decoupling techniques for wave equations with dynamic boundary conditions

In this note we introduce a decoupling technique for operator matrices with "non-diagonal" domains on "coupled" spaces which greatly simplifies the study of Cauchy problems stemming from wave equations with dynamic boundary conditions