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.

中文翻译：

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扰动的自治和非自治发展方程的最大正则性

本文的主要目的是利用系统理论的思想研究Banach空间中某些摄动的自治和非自治演化方程的最大\（L ^ p \） -正则性的概念。我们主要考虑两类扰动：Miyadera–Voigt扰动和Desch–Schappacher扰动。我们介绍了在这种摄动下可以保留最大\（L ^ p \） -正则性的条件。我们通过一些应用来说明我们的结果，尤其是在非自反空间中的PDE示例。