One of the most important systems for understanding chemotactic aggregation is the Keller-Segel system. We consider the time-fractional Keller-Segel system of order ∈ (0, 1). We prove an existence result with small initial data in a class of Besov-Morrey spaces. Self-similar solutions are obtained and we also show an asymptotic behaviour result.
K E Y W O R D SBesov-Morrey, chemotaxis aggregation, fractional derivative, Keller-Segel model, spaces M S C ( 2 0 1 0 ) 26A33, 35A01, 35B40, 35K45, 35K55, 35Q92, 35R11, 92C15, 92C17
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.