On perturbations of eventually compact semigroups preserving eventual compactness (Q1764622)

The author studies the compactness of the solution semigroup for some partial functional differential equations in the \(L^p\)-context for \(p\geq 1\). He assumes that the semigroup generated by the undelayed part is compact and that the delayed part satisfies some conditions which make use of the Miyadera-Voigt perturbation. The author proves that the solution semigroup is eventually compact which is used to investigate the spectral analysis of the solution. The numerical treatment is also studied.