On the maximal regularity for perturbed autonomous and non-autonomous evolution equations

The main purpose of this paper is to use ideas from systems theory to investigate the concept of maximal L-p-regularity for some perturbed autonomous and non-autonomous evolution equations in Banach spaces. We mainly consider two classes of perturbations: Miyadera-Voigt perturbations and Desch-Schappacher perturbations. We introduce conditions for which the maximal L-p-regularity can be preserved under these kinds of perturbations. We illustrate our results with some applications, in particular with an example of PDE in non-reflexive spaces.