Abstract

In this article we provide new insights into the well-posedness and maximal regularity of systems of abstract evolution equations, in the framework of periodic Lebesgue spaces of vector-valued functions. Our abstract model is flexible enough as to admit time-fractional derivatives in the sense of Liouville-Grunwald. We characterize the maximal regularity property solely in terms of R-boundedness of a block operatorvalued symbol, and provide corresponding estimates. In addition, we show practical criteria that imply the R-boundedness part of the characterization. We apply these criteria to show that the Keller-Segel system, as well as a reactor model system, have Lq - Lp maximal regularity. (c) 2024 Elsevier Inc. All rights reserved.