Global existence and asymptotic behavior of classical solutions to a fractional logistic Keller-Segel system

In this paper we consider a fractional parabolic-elliptic Keller-Segel system with a logistic source on R-N. First, we establish the regularity of weak solutions of the fractional parabolic equation, using blow-up arguments combined with Liouvilletype theorems. Next, by the semigroup method and regularity results we prove the local existence and uniqueness of classical solutions. Moreover, the global existence and boundedness of classical solutions for given initial data are obtained under some conditions. Finally, we show the asymptotic behavior of the global solutions with strictly positive initial data. (C) 2019 Elsevier Ltd. All rights reserved.