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arXiv · 1810.08964

Maximal $L^p$-regularity for perturbed evolution equations in Banach spaces

A. Amansag·H. Bounit·A. Driouich·S. Hadd
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Abstract

The main purpose of this paper is to investigate the concept of maximal $L^p$-regularity for perturbed evolution equations in Banach spaces. We mainly consider three classes of perturbations: Miyadera-Voigt perturbations, Desch-Schappacher perturbations, and more general Staffans-Weiss perturbations. We introduce conditions for which the maximal $L^p$-regularity can be preserved under these kind of perturbations. We give examples for a boundary perturbed heat equation in $L^r$-spaces and a perturbed boundary integro-differential equation. We mention that our results mainly extend those in the works: [P. C. Kunstmann and L. Weis, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 30 (2001), 415-435] and [B.H. Haak, M. Haase, P.C. Kunstmann, Adv. Differential Equations 11 (2006), no. 2, 201-240].

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A. Amansag, H. Bounit, A. Driouich, S. Hadd. 2018-10-21. Maximal $L^p$-regularity for perturbed evolution equations in Banach spaces. https://arxiv.org/abs/1810.08964

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