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Apr 22 at 12:30 comment added ahdahmani Even though too late but I would like to mention further referenes that I find very intersting. Kisyński, J.. "Sur les opérateurs de Green des problèmes de Cauchy abstraits." Studia Mathematica 23.3 (1964): 285-328. <eudml.org/doc/217075>. Contrarily to most of the other results, this paper treats operators with time dependant domains. Gregor Nickel's thesis and papers with Rainer Nagel contain some intersting examples that emphasise the difficulties in the non autonomous case.
Nov 23, 2023 at 8:19 comment added Hannes I am late to the party and apparently you have found something sufficient for your needs, but I would like to mention Section 3 in $L^p$-maximal regularity for non-autonomous evolution equations by Arendt, Chill, Fornaro and Poupaud which, I think, fits your problem description well
S Jul 13, 2023 at 21:43 review First answers
Jul 13, 2023 at 21:46
S Jul 13, 2023 at 21:43 history answered Peter Wacken CC BY-SA 4.0