Maximal $L^p$-regularity for perturbed evolution equations in Banach spaces
Abstract
The main purpose of this paper is to investigate the concept of maximal -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 -regularity can be preserved under these kind of perturbations. We give examples for a boundary perturbed heat equation in -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].
Keywords
Cite
@article{arxiv.1810.08964,
title = {Maximal $L^p$-regularity for perturbed evolution equations in Banach spaces},
author = {A. Amansag and H. Bounit and A. Driouich and S. Hadd},
journal= {arXiv preprint arXiv:1810.08964},
year = {2018}
}
Comments
38 pages, 0 figures, the work use feedback theory of infinite dimensional control systems to prove results on Maximal regularity for linear perturbed evolution equations