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

Abstract

In this paper we consider a fractional parabolic–elliptic Keller–Segel system with a logistic source on RN. First, we establish the regularity of weak solutions of the fractional parabolic equation, using blow-up arguments combined with Liouville-type 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.