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

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Ibn Zohr University, Hay Dakhla, B.P. 8106, 80000, Agadir, Morocco

    Ahmed Amansag, Hamid Bounit, Abderrahim Driouich & Said Hadd

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  1. Ahmed Amansag
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  2. Hamid Bounit
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  3. Abderrahim Driouich
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  4. Said Hadd
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Correspondence to Abderrahim Driouich.

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Amansag, A., Bounit, H., Driouich, A. et al. On the maximal regularity for perturbed autonomous and non-autonomous evolution equations. J. Evol. Equ. 20, 165–190 (2020). https://doi.org/10.1007/s00028-019-00514-8

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