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

Azevedo Joelma | Zendy; Cuevas Claudio | Zendy; Henriquez Erwin | Zendy

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

Author(s) -

Azevedo Joelma,

Cuevas Claudio,

Henriquez Erwin

Publication year - 2019

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.201700237

Subject(s) - mathematics , class (philosophy) , order (exchange) , chemotaxis , pure mathematics , mathematical analysis , computer science , economics , artificial intelligence , biochemistry , chemistry , receptor , finance

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.

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