Existence and asymptotic behaviour for the time‐fractional Keller–Segel model for chemotaxis

Joelma Azevedo, Claudio Cuevas and Erwin Henriquez

Mathematische Nachrichten, 2019, vol. 292, issue 3, 462-480

Abstract: 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 α∈(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.

Date: 2019
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