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

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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… Click to show full 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.

Keywords: asymptotic behaviour; fractional keller; time fractional; keller; keller segel

Journal Title: Mathematische Nachrichten
Year Published: 2018

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