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The main purpose of this paper is to use ideas from systems theory to investigate the concept of maximal Lp\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$L^p$$\end{document}-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 Lp\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$L^p$$\end{document}-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.
Journal of Evolution Equations – Springer Journals
Published: Mar 22, 2020
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