Global existence and asymptotic behavior of classical solutions to a fractional logistic Keller–Segel system. (December 2019)

• Record Type: Journal Article
• Authors: Zhang, Weiyi; Liu, Zuhan; Zhou, Ling
• Is Part Of: Nonlinear analysis. Volume 189(2019)
• Publication Date: 2019-12
• Subjects: 35K51 -- 35R35 -- 92B05 -- 35B40; Fractional Keller–Segel system -- Regularity of weak solution -- Classical solution -- Global existence -- Asymptotic behavior; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111624
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: 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 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.